Is there an optimal time to promote from the villager class?

In most Fire Emblem games, there's an "optimal" time to promote - that is, you hit level 20 with the base class, and then you promote the unit so that it keeps 20 levels worth of stat growth.

Does stat growth work the same way in Fire Emblem Echoes: Shadows of Valentia? (and is the villager --> main class process a "promotion"?) Can I try to max out the villager class, and then promote the unit so that they have the max stat growth? Or do their stats reset when they choose a main class?

Technically, the optimal time to class a Villager is at the level cap, 20. However, since Villagers are so weak, it may be best for you to class them sooner, in order to fill the gaps in your team sooner, as the soft cap in experience gain makes the grind to 20 take a while.

This guide goes pretty in-depth about the subject.

First off, there is definitely less of a reason to wait to promote than in previous Fire Emblem games.

This is thanks to how stats are bumped up to a unit minimum and because it's harder to gain experience (EXP) at high levels in Fire Emblem: Shadows of Valentia. Compared to previous Fire Emblem games it is thus a bit of a no-brainer that you might want to promote classes immediately.

However, you may still want to wait before you promote - but know that if you do it'll take a lot of grinding in order to see a real benefit.

Gaining EXP at levels 18 through 20 will take much longer for a small stat gain than if you promote early and gain EXP as a newly-promoted, fresh-faced level 1 class.

A specific example of the results of holding off on a class promotion are also given in that guide:

I have Jesse, a Myrmidon, at Level 11. I can promote him now to a Dread Fighter, but should I wait? His stats already pass the Dread Fighter minimum stats:

Promote at Level 11 -- HP: 39 (bumps to 40) ATK: 19 SKILL: 20 SPD: 28 LCK: 19 DEF: 14 RES: 7 MOV: 5 (bumps to 7)

I decide to get him to a Level 20 Myrmidon before promotion, and here are his stats now:

Promote at Level 20 -- HP: 43 (bumps to 44) ATK: 22 SKILL: 23 SPD: 35 LCK: 22 DEF: 16 RES: 7 MOV: 5 (bumps to 7)

As you can see, his stats as a Level 1 Dread Fighter will be notably better if I wait until Level 20 before promotion, but as noted earlier his EXP gain as a high level Myrmidon will be less than his EXP gains as a fresh-faced Level 1 Dread Fighter. If you are willing to tough it out, it can definitely be worth waiting to promote.