Y’all. After SIX months of searching, applying, interviewing... I FINALLY got a job offer. It is such a relief. But I’m not sure if it’s the best fit for me. Here is where I am wondering what a man would do:

I got an offer from Job A. But, I think Job B is the right job for me. I just had a second interview with Job B late last week and they are already checking my references this week. Do I call/email Job B and let them know that I got an offer from Job A and ask about their hiring timeline (and risk looking impatient bc they are clearly trying to move fast BUT potentially make them realize I am sought after so they should want me too)? Or do I just let it be and only use the Job A offer as a bargaining tool in the event I actually get an offer from Job B?

If it matters, both jobs are in the same (insanely huge) organization.

Edit: I have a decent amount of time to sit on the Job A offer. So contacting Job B wouldn’t be because I need them to speed up their process (though it would be nice); the main goal would be to let them know that other people in their org want me so they should too!