Is this pretty typical, or have I missed something?
Yes, just as in many good games (tabletop or otherwise), you are given a finite resource which you must learn to economize. It's all part of the game!
At low levels, it's pretty easy to run out of spell slots, you only have 2 of them so it is up to you to manage them and make the most out of what you have. Even as other spellcasting classes such as Bard and especially Warlock, you really need to think about what sort of situations you want to spend your precious 2 1st-level spell slots on.
Without spell slots, you have other options for offense but going into melee with your armorless self is less than advisable so your best bet is to use your cantrips just as you are doing right now. They might look a bit underpowered to you at first, but that is because these level 0 spells give up damage for a slight mechanical benefit. Shocking Grasp prevents your target from taking reactions(thereby allowing you to get away safely), Ray of Frost slows down your target by 10 ft, Fire Bolt sets things ablaze, even Sacred Flame negates cover. These cantrips also increase in damage as you reach higher levels (usually at 5th-level so it is still a ways off)
Don't worry, 2nd-level will come faster than you might expect. Then you'll have 3 1st-level spell slots to contemplate spending.
As a final note, and this may be nothing but if you find yourselves struggling for resources every session, remember: a long rest isn't a "session ender", you can take long rests in the middle. In my group, we have fun over the logistics like bedrolls and sharing them because one guy didn't have one.
There are also guidelines in the DMG on the experience earned in an adventuring day, found in page 84. I felt like I should mention this because it's odd that you've had 5/6 encounters and still haven't gotten to 2nd-level.
You should totally scale the single-monster encounters to make them memorable for everyone. You have multiple options for that.
Lair actions
If your single monsters are bosses or the like, you can give them lair actions. Just look at examples like the dragon ones (starting at MM 86). Rambling terrain, furious waterfalls, tempest winds, make your choice.
Modify your monsters
Read the chapter Modifying a Monster in the DMG 273. You can adjust simple things like giving immunity to a certain type of damage to the monster, give it a flying distance, give it better weapons (maybe even magical lootable ones!), or give it additional features (pick one from the DMG 280!).
Making a bigger version of a monster can also be a thing (like modify a medium monster into a large one). This will increase its hit points and also allow it to do more damage using weapons (x2)! (see Step 11. Damage DMG 277-278)
You can then re-calculate the challenge rating of your monster and make sure it is appropriate for your party !
Add minions
Powerful monsters don't always act alone. They often have hordes of minions at their command, and even bodyguards or lieutenants! If you don't want to add too many monsters to encounters, as you mentioned, you could give a try to the latter options! Simply add one or two less/much less powerful monsters to the fight, and this should rise the overall challenge rating of your encounters!
Best Answer
Early enemies become more dangerous
A goblin has an AC of 15, which is much higher than the DMG-recommended AC for a foe of its CR. In exchange, it has extremely low HP. Let's consider a level 1 melee character. With 7.5 (1d8+3) damage from a longsword, the character will, on average, barely kill a goblin if they hit. If the goblin instead has 12 HP, it will take two hits (around 4 attacks) to down it, doubling the length of already-dangerous low-level combats.
Control becomes more powerful
The fighter takes up to twice as long to kill an enemy with maximized HP. The wizard casts hypnotic pattern and it is exactly as effective as it was against enemies with normal HP. In my experience, the game is already slightly in favor of full spellcasters, and maximizing HP would exacerbate the situation.
Certain spells are much less effective
As @DanielZastoupil pointed out, sleep directly affects HP, and thus is far less effective against maximized HP enemies. Against a room full of goblins with 7 HP, sleep has a 96% chance of affecting at least two of them, a 65% chance of affecting at least three, and a 17% chance of affecting at least four. If a goblin's HP is 12, the chances drop to 42%, 0.4%, and 0% for at least two, three, and four, respectively. In my experience, sleep is a large part of low-level bard, sorcerer, and wizard effectiveness.