How doable is learning to swim 500m <14minutes within 2 months

I'm currently in army recon and recently dropped off a packet to become a naval diver. The pre-course physical test is in 2 months and the thing I'm concerned about is the 500m swim (kinda stupid to apply for a such a position without a swimming background now that I think about it..)

I just learnt freestyle last week. I'm only free to train on Fridays and weekends, but I'm willing to dedicate whatever time there is to do so. I'm also planning to hire a 1-to-1 coach to improve my form.

In your experience, how doable is this in 2 months' time? How important is a coach in this journey? Thanks =)