No, but higher-level class feats can
The Focus Spells rules (CRB 300) state:
You automatically gain a focus pool of 1 Focus Point the first time you gain an ability that gives you a focus spell.
The key phrase here is "the first time" for two reasons:
It specifies when you initially gain a focus point (when you first take the Domain Initiate feat, in your case)
It specifies that you gain a focus point from this source only the first time you gain this ability
So no, taking Domain Initiate two or more times will not grant you additional focus points beyond the first (though it will give you access to more focus spells to use with that focus point).
How can I get more focus points?
This is where other class feats come into play. Consider Advanced Domain, an eighth-level cleric class feat:
Your studies or prayers have unlocked deeper secrets of your deity’s domain. You gain an advanced domain spell from one of your domains. Increase the number of Focus Points in your focus pool by 1.
What about through archetypes or multiclassing?
You can get more focus points from later taking other distinct feats or abilities that explicitly grant a focus pool according to this clause from the Focus Points from Multiple Sources sidebar (CRB 302):
If you have multiple abilities that give you a focus pool, each one adds 1 Focus Point to your pool.
A low-level example of this is the first-level monk class feat Ki Rush, which includes the following:
You gain the ki rush ki spell and a focus pool of 1 Focus Point.
You already have a focus pool granted to you by the Focus Spells rules (because you received a focus spell from Domain Initiate). The Focus Points from Multiple Sources rules clarify what happens when you get additional abilities that grant a focus pool/point:
If this happens, you have just one focus pool, adding all the Focus Points together to determine the total size of your pool.
If you had a character with Domain Initiate and a focus pool of 1 point, and that character later somehow took Ki Rush, then you would have a focus pool of 2 points.