shrug
In other editions, a 1st level character has exactly one (1) attack.
Here, you have up to three.
Other than that, I don't believe the -10 penalty is intended to be encountered in practical play. I simply assume you pick up a way to lessen or circumvent it soon enough.
Compare this to spells, which appears to be mostly or entirely unchanged, and the answer to the OP's concern becomes obvious.
I don't see how a fighter would do so meaningfully at 1st level. I suppose you could use an Agile weapon, but that only changes the hit chance to 65%, 45%, and 25% respectively. But Agile weapons tend to do less damage.
On top of that, those numbers are for the fighter, who ruins the curve so to speak. No other class starts with Expert weapon proficiency. Non-fighters are looking at 55%, 30%, and 5% (55%, 35%, and 15% with Agile) base hit rates. Asserting that they get three attacks is somewhat misleading when the second attack has about a 1 in 3 chance of landing, and the third attack amounts to hoping for a natural 20.
I'll grant that there are a few outliers; the Flurry Ranger with an Agile weapon being the prime candidate IMO. That build will want to attack with all three actions every chance they can get. However, it is reliant on Hunt Prey (which costs an action) meaning that it's closer to two attacks. If the prey is tough enough to take 5 attacks from the ranger to kill, you're still only looking at 2.5 attacks per round even under optimal conditions (you don't need to waste an action to Stride in order to get into melee).
It looks to me like, even being generous, in most circumstances you're looking at one and a half attacks. You might roll three d20s on your turn, but the second attack is unreliable, while the third is a shot in the dark. Effectively, it's closer to one and a half. IMO, optimized play involves finding alternate uses for your third (and possibly even your second) action that don't suffer MAP. That's if you even have the actions available, as melee might need to spend a few actions to get into position. For most builds, using all three actions to attack is likely to be a sub-optimal tactic.
Spells may be largely unchanged (I haven't done a thorough read through of the spells chapter yet and couldn't say). However, the warrior classes generally were only improved from 1 attack to 1.5 from what I can see. On top of that, cantrips were greatly improved. So while the high end of warrior damage at 1st level was increased, the same can be said for the low end of caster damage. Which isn't true parity, but is a rough sort of equivalence.
I agree with you that warrior types are probably in a stronger place at 1st level compared to casters, but I just don't see the difference in power being as large as you seem to be suggesting it is.