I figured it could be a combination of nominalizer "の" and object marker "を," the action being 後悔する
Your understanding is correct.
To break this down a little further:
会ったの is a noun meaning something along the lines of the English "having met (you)" or "that I met you". We can reasonably assume the subject is the speaker, and the object is probably the person that said speaker is speaking to, although we would need more context to be sure of that.
今は means "now", but because this is a contrastive は, the important thing here is that the speaker is emphasizing that they regret meeting someone now, as opposed to some previous point in time when they didn't regret it.
後悔してる 後悔 is a straightforward する verb meaning regret, and the
している) just means that the speaker is currently doing said regretting.
In short, if we assume the object of
会う is the person being spoken to, the sentence means:
Now I'm regretting having met (you)
To answer your questions:
- In a lot of casual speech particles (including
を) are dropped, but I assume that's not what you're asking. Grammatically, there's no basis for you to drop
- You could make the object of
会った explicit, but the correct particle is not
に. It would be
- Incidentally, if you want to use
のだ for emphasis/explanatory purposes, it would be
後悔してるのなんだ, which is unnatural.