If we have only one possible hen how long can she stay by herself until we get more pullets? We did not plan on keeping any roosters so this is very unfortunate and not quite sure what to do from here.
I would get more as soon as possible.
I have two small dog crates, plus a bigger one, I use for brooding chicks. So if it were me, I would be able to put a new batch of chicks - ideally from the same source, for biosecurity reasons - nearby enough that they can see and hear each other, but not touch. That way at least she would have some company if you are able to re-home the cockerels fairly soon ish. As long as they are still small, it shouldn't be too much of a problem for them to be together, but I would think by the time they all go outside, I personally would want the cockerels in a separate grow-out pen.
You can kind of finagle the timing to bring them out depending on your climate and things like that. Like if you have one pullet who is older, you would probably keep her inside longer while the other chicks grow out, so say she's about 10-11 weeks, but the rest are only about six, and the weather is nice, that could work for them all to integrate in the coop at that point, if you haven't already integrated them in the brooder by that time.
Last year I brooded chicks together that were about two weeks apart, that had its challenges but it was fine. I can't remember but I think they went outside when they were 8 and 10 weeks? or 7 and 9? respectively. 4-5 weeks is a much bigger age / size gap, so I would honestly hurry out and get more chicks ASAP, along with finding out if anyone can either take extra males, or else making a plan to grow them out yourself.

I have heard you want to process before they crow anyway, so what, 12-16 weeks only and they can be dinner.