A company that I was interviewing is telling me that they really like me but I would have to wait for a few weeks until they finish interviewing other candidates. While I don't want to interrupt their process, is there a way that I can get them to short circuit their process? I already let one offer pass by (from another company) because it frankly did not check all the boxes. I am available immediately but they don't know that yet.
There's really no good way to speed up the process. If you press them, you may seem desperate or even just annoying.
Having to interview all of the candidates is very common and is probably a good practice if the interviews are already lined up. They don't risk missing out on an unexpectedly great candidate with a minimum of effort.
There's only one possible way I can think of to speed them up and that's to have another offer on the table. And I mean a real offer. In writing, that you actually want.
In other words, keep looking, keep interviewing and remember:
Unless you get an actual offer in writing, you don't have an offer. It doesn't matter if the hiring manager and even the CEO tell you they're hiring you. Unless you have an actual offer, keep looking.
Only one thing is clear--they are keeping their options open. You should too. Keep interviewing and get excited about other opportunities. If this one loops back, you can decide when the offer comes through. You have no offer, no terms, nothing to bank on.
If you try to push forward you will lose leverage in salary negotiation and gain nothing in moving them faster. Would you like the job for 20% less than market value?
The fact that you're available right away probably doesn't concern them. They're taking a few more weeks to interview, what's wrong with 2 more for notice?
There is only one thing you can do to speed up their decision process in a favourable way. Find another job.
Once you have another job offer, then it's quite fair to contact them explaining that you have another job offer, that if they are able to make an offer within the next 24 hours it will be looked on favourably, otherwise you will alas, be off the market.
They may say a straight no. If you are their best candidate, they may decide that they don't want to lose you, and shorten the selection process.