I applied to a startup job on Monday and realized today that the hiring manager is connected via LinkedIn to one of my mentors. I haven’t heard back yet so should I ask my mentor for an introduction? How should I ask my mentor?
I haven’t heard back yet so should I ask my mentor for an introduction?
Seems that it has been only 2 days since you applied this past Monday.
Thus, I suggest you wait a bit more before considering replying or doing follow-up. The "rule-of-thumb" that is often suggested on this Community is to wait at least a week before doing so, as doing it before could come as desperate or annoying to the recruiter or contact.
Furthermore, the fact that they are "connected via LinkedIn" doesn't mean they keep in touch, or have spoken recently; asking your mentor to introduce you may prove ineffective if this is true.
Before considering asking your mentor for such thing, first ask him/her if they are still in touch, to see if this idea is viable.
You're much more likely to get an interview if you have an introduction!
Lever, a recruitment marketing company, did a study recently and found that 1 of every 16 referred (or introduced) candidates is hired, while only 1 of every 152 people who apply through applicant tracking systems are hired.
You can go with what I've shared or read more about the Lever study here.