[RPG] Once you take a Prestige Class, can you advance your base class later

Your GM is correct. Until you are higher level you are not able to cast higher level spells. The entire point of prestige class entry requirements is to gate entry to more experienced characters, and your interpretation basically reduces to just saying "an arcane spellcaster" which if that's what they meant, it's what they'd say. You need to actually be able to cast the spell, so you need appropriate level + high enough stat + correct class + not having swapped out your spellcasting ability for some other ability and so on.

Remember that this is supposed to represent some kind of in game qualification.

"Welcome to the Guild of Master Evokers! So you want to join, eh?"

"Yes!"

"OK, show us your stuff, cast something big - you know, a fireball or whatever."

"Well, I can't now - but I have the ability to one day!"

"What does this look like, Hogwart's? Don't let the door hit you in the ass on the way out."

In this context, "able to cast" and "ability to cast" mean the same thing. The designers' neglecting to use the exact same verbiage for every writeup is... pretty typical, actually, and not indicative of any deliberate nuance.

Also there seems to be a misunderstanding about a high stat possibly letting you cast higher level spells early - this is not the case. "In addition to having a high ability score, a spellcaster must be of a high enough class level to be able to cast spells of a given spell level." -d20PFSRD

There is nothing similar to Practiced Spellcaster for spells known/per day and highest spell level. Such a feat would probably be overpowered.

There are ways to enter mystic theurge without three levels burned on each side, i.e. before 6th level. Normally I am strongly opposed to such “early entry” tricks, but in the case of the mystic theurge, they are largely necessary as the mystic theurge is nothing but a trap without them.

You’ll definitely need one level of each class, obviously, so you have something to progress, and you’ll never get that back, unfortunately. So even if you could enter mystic theurge earlier, spending a level on each class is necessary to actually benefit from the class. Also note that if you expect your campaign to reach levels more than 10 above whenever you get to into mystic theurge, you’re not going to be able to continue progressing both classes,¹ which is a big ouch. If you expect your campaign to go much beyond there, I strongly recommend against mystic theurge unless your DM houserules you to be able to take more than 10 levels of mystic theurge (and ignores the atrocious epic mystic theurge progression).

For the sake of argument, I’m going to assume you are going for an archivist/wizard/mystic theurge, as this is the best choice available. I assume you take the archivist level(s) first then wizard levels, and that you favor wizard over archivist. In most cases, archivist and wizard could be swapped for any other divine and arcane spellcasting classes, respectively, and order and number of levels is flexible so long as you have one of each and the totals are the same. I’ll note any exceptions.

Meeting mystic theurge spellcasting requirements at ECL 2

Note that, due to the skill rank requirements on mystic theurge, all of these are fail to get you into the class. These are ways to get the necessary spellcasting by ECL 2, but without some way of dodging the skill rank requirements, that doesn’t actually get you in. Cheesing the skill rank requirements is a lot harder, and requires much more dubious assumptions (e.g. a high-level bard willing to help you out).

Improved Sigil (Krau) Illumian: race and 1 feat, ambiguity (Races of Destiny)

An illumian can take Improved Sigil (Krau) to apply a free Heighten Spell to a number of spells. The idea is to get 1st-level spells on each side, and use Krau to make a spell on each side 2nd-level and thus qualify for mystic theurge.

There’s a rule ambiguity here about whether or not being able to cast 1st-level spells from a new class qualifies as a “new level of spells” when you could already cast 1st-level spells. If yes, you can take it at 1st level, e.g. archivist 1, and then take another class, e.g. archivist 1/wizard 1, and switch your chosen spells to be one archivist spell and one wizard spell. Then you qualify for mystic theurge.

If not, you have to take Improved Sigil (Krau) at ECL 3, e.g. archivist 1/wizard 2, so you can pick spells from each from the get-go. Which is the best you can do without skill rank shenanigans, so no huge loss unless you are really trying to cheese to the hilt.

Precocious Apprentice & Southern Magician: 2 feats, dubious rules (Complete Arcane, Races of Faerûn)

Setting-specific, and within that setting, specific to Mulan humans, which may or may not be problematic depending on whether or not you are playing in the Forgotten Realms.

This approach requires that you take the arcane spellcasting level first.

Precocious Apprentice allows you to cast a single 2nd-level arcane spell. Southern Magician allows you to cast an arcane spell “like” a divine spell (and vice versa), but whether that’s good enough to qualify for mystic theurge is unclear. For what it’s worth, Wizards Customer Service says no.

Note that this, if it works, allows a wizard to qualify for mystic theurge without any divine spellcasting levels at all. This either means the benefit of mystic theurge is wasted, or you get to advance wizard twice as fast as it’s also a divine spellcasting class. Even if your DM is crazy enough to let you, I cannot recommend against that strongly enough.

Sanctum Spell: 2 feats, rather difficult timing requirements (Complete Arcane)

You must either be human or some other bonus-feat-granting race, or be playing in a campaign with the Flaws variant from Unearthed Arcana, if you want to get enough feats in time to do this optimally.

Sanctum Spell requires one metamagic feat, any metamagic feat. Once you have that, you can take Sanctum Spell, which is basically a free single-level Heighten Spell effect if the spell is cast within your sanctum. This means that in order to go from e.g. archivist 1/wizard 1 to archivist 1/wizard 1/mystic theurge 1, and again for getting archivist 1/wizard 1/mystic theurge 2, you have to be in your sanctum during level-up, or get your DM to agree to it based on your potential to cast 2nd-level spells. Good luck.

Earth Spell: 3 feats (Races of Stone)

Earth Spell requires Heighten Spell and Earth Sense, basically allowing you to have a free extra level when using Heighten Spell. Heighten a cantrip and an orison with it, and you get 2nd-level spells on each side. Three feats that early requires Flaws or shenanigans beyond the scope of this answer.

That said, this pretty much just works, which is a big advantage over the previous answers.

Meeting all mystic theurge requirements at ECL 3

This is far easier because it gives us another feat to play with, a feat that can be taken after you have both types of spellcasting, and it also allows us to get the necessary skill ranks to trivially meet the mystic theurge’s requirements.

Improved Sigil (Krau) Illumian: race and 1 feat (Races of Destiny)

Just mentioning this again: if the rules are interpreted against us (which strikes me as the more likely interpretation), Improved Sigil (Krau) becomes an ECL 4 trick rather than ECL 3. Still a good option.

Precocious Apprentice & Alternate Source Spell: 2 feats (Complete Arcane, Dragon vol. 325)

This approach requires that the arcane spellcasting class come first.

Precocious Apprentice gives you a 2nd-level arcane spell, Alternate Source Spell makes it divine. Note that the wording of Alternate Source Spell is far more amenable to this use than Southern Magician, it just requires that you can already cast divine spells. So you go e.g. wizard 2/archivist 1 so you can take it, and use it on your Precocious Apprentice spell.

Still runs into the typical arguments revolving around using Precocious Apprentice this way.

Meeting all mystic theurge requirements at ECL 4

This is easy, because it means you have three levels on one side, and thus native access to 2nd-level spells.

Alternate Source Spell: 1 feat (Dragon vol. 325)

As, e.g., archivist 1/wizard 3, Alternate Source Spell allows your 2nd-level arcane spells to be 2nd-level divine spells, and now mystic theurge can advance both archivist and wizard.

Southern Magician: 1 feat, rules ambiguity (Races of Faerûn)

Compared to Alternate Source Spell, this has the advantage of not being from Dragon, but the disadvantage of having rules that confuse whether or not it actually works, as well as awkward setting requirements. Otherwise, it works pretty much the same way.

Honorable Mention: Early entry to arcane hierophant (Races of the Wild)

Arcane hierophant is a prestige class that advances both druid and an arcane spellcasting class. This is a big deal because between it and mystic theurge, you have 20 levels of dual-progression, answering the big “what now?” question that usually happens when you finish mystic theurge.

The same tricks as above for meeting the arcane hierophant’s spellcasting requirements still work, and taking a single level of druid gets you the Animal Companion, but the Trackless Step requirement is trickier. The easiest way to get it is by being one of the bamboo spirit folk from Oriental Adventures.

Other Honorable Mention: Early entry to Fochlucan lyrist (Complete Adventurer)

Fochlucan lyrist requires a large number of skills, 1st-level arcane and 1st-level divine spells, bardic knowledge, and most vexingly, evasion and knowledge of the Druidic language. It progresses both arcane and divine spellcasting on 10 out of 10 levels.

Bardic knowledge as such only comes from the bard class, and since Fochlucan lyrist requires 1st-level spells, that would mean two levels in bard. A level of cloistered cleric, however, arguably satisfies that requirement, since its lore feature is equivalent to bardic knowledge. Ask your DM on that one. Alternatively, divine bard could allow you to use bard as your divine side, which might be nice so you can be closer to Charisma-only (using sha’ir or sorcerer as your arcane side). Note that divine bard requires a little commitment to Wisdom, up to 16 in order to cast 6th-level divine bard spells.

Evasion is simultaneously easier and harder: you can buy it. A ring of evasion is 25,000 gp, not really a viable investment until 10th level or so, but it does get you into the class. Per the Dungeon Master’s Guide, once you take your first class level, you no longer need to meet the requirements: if you lose or sell the ring, you not only keep your Fochlucan lyrist class features, you also keep your right to continue taking levels in it. Check with your DM first. If you want it a little more permanently, or before you can afford 25,000 gp, you could take Shape Soulmeld (impulse boots) and Open Least Chakra (feet), both from Magic of Incarnum, which gets you both uncanny dodge and evasion. Unfortunately, Open Least Chakra still requires 6th level. Beyond these, divine oracle from Complete Divine offers evasion-even-in-armor at 2nd and progresses one class’s spellcasting, anyway (oddly enough, despite the name, it can progress arcane spellcasting).

Finally, knowing Druidic is trivial if your other half is druid, but otherwise you will have quite a few difficulties. See here for some ideas on how to tackle that.

1. _{Unless you are a bard or druid; see arcane hierophant and Fochlucan lyrist.}