Ultimately, the frequency at which abiogenesis occurs is 1/N.
It may be the case that N is small enough that the universe is positively teaming with life.
Or it may be the case that N is so unfathomably large that the odds are exceedingly small that abiogenesis occurs even once during the lifetime of the universe, and the universe just happened to get lucky.
But until we have some other confirmed, observed instance of abiogenesis, we can say nothing about N other than its lower bound is pretty large.
And I don't think we can pile probabilities on top of probabilities to say, "Well, we have no way of knowing how large N is, so I'm going to just bet that it's medium-sized."
[0] to the extent that events across vast spans of space can be said to be ordered
None of this is any kind of _hard_ proof of course, it's just attempting to reason through what we expect without having enough data to prove either way.
If we conclude for some reason that we are the first, with enough evidence, sure, like you say someone has to be first.
But with so little data, the priors for "are we first or are we just missing the others" just have to be tilted heavily away from "we're first".