[RPG] How to help a new player feel safe taking risky actions in-game

I think this shouldn't be a dilemma for you, the GM. It should be a dilemma for the players.

If a player can craft a super-secret Alchemy Stone which will single-handedly turn the tide of battle against the forces of evil, then they will want to craft it. However, if it takes two months of intensive work to create, then the forces of evil are still moving against them in the meantime. This causes an interesting issue for the players to solve in-game. Do they take the time to build the super-secret Alchemy Stone? Do the forces of evil know that they are attempting this and try to stop them? Perhaps that would be an interesting session idea; the one character is trying to craft the MacGuffin, while the others defend his efforts from the adversary.

If it's less plot-related or dramatic crafting (like just a decent potion or other "nice-to-haves" for the characters), then you can consider simply allowing the following understanding: every night before bed, the character spends an hour performing whatever their craft is. You don't have to play this out every time. Then, after an agreed upon number of in-game days, they get whatever their trinket is. Even this is somewhat of a stretch, though, since for most crafts it would take at least an hour just to set up their equipment properly.

With that said, this is the very reason that crafting skills generally don't mix very well with an adventuring party if you're attempting to be realistic about the time frames. That's why every fantasy video game simply glosses over the crafting with a blacksmithing sound ("clang-clang-clang") and perhaps a very short timer. The amount of effort it takes simply to smith a sword is enormous, never mind whatever complex things your PCs are likely attempting. So you can either compromise your realism slightly in order to maintain the fun of the game, or you can let it be an interesting in-game dilemma.

To address the specific issue mentioned in the comments below: If you want your Wizard to be able to scribe spells into his spellbook faster but don't want to directly manipulate the rules-as-written (RAW), let them go on a quest for a magic quill which allows faster scribing or something. This would be a (hopefully) interesting in-game solution to a problem that the characters face.

You seem to be looking for an out-of-game, sort of meta-game solution to what is ultimately an in-game problem. And it's in-game problems which make games interesting. No amount of meta-game shenanigans will change the fact that in the real world it takes a week to simply forge a sword, so you will need to either bend reality, change the rules, or trust your players to handle it. For me personally as a GM, I would never force my Wizard to spend an entire day putting a new spell in his spellbook, because it's my opinion that the RAW are not the most important thing. My job as a GM is to remove obstacles that are in the way of everyone having fun.

The easiest way to emphasize your casters in the early game, is to throw in lots of relevant skill checks, particularly knowledge or spellcraft checks. Almost any spellcaster is going to have relevant skill modifiers, and it proves their place in the party.

A related option is challenges tailored to make spells useful. A small item you need is on the far side of a chasm? Summon Nature's Ally or Mage Hand can help with that. Having ambient magic, or an arcane trail to be tracked with Detect Magic also calls out your casters.

Also, it's been my experience that Druid is one of the better low level caster classes, with cleric because of free swapping in of Summon Nature's Ally spells, reasonable combat ability (3/4 BAB, d8 HD, not terrible armor, buff spells), and their selections of durable spells, such as Produce Flame and Call Lightning.

For the Archivist play to their skills and their Dark Knowledge ability. Throw in a fair number of the types of enemies Dark Knowledge helps against, and they should feel pretty useful.