Sharing because I’ve gone through the process (except your experience & interest in SaaS will give you higher chances of interview, given it’s the main space right now)
VC funds don’t necessarily put up job postings always
You need to figure out folks from each fund who are VP/Principals and look into SaaS and reach out to them via cold emails (typically their emails should be on LinkedIn or the fund website)
Given your background, you should be able to hear back where they are hiring given your profile.
One thing that works even better - reach out to people who have been in the same undergrad or company, higher conversion there
Make a list of all VCs where you are interested and just do this, it’ll work.