Ah, a pet peeve. Irvine sucks. It may be ok for you or me but I certainly wouldn't recommend it to anyone out for a Sunday outing with their family.
The Google map shows a route along 2nd Ave, but as it's been pointed out this street is barred by a gate. The gate(s) makes sense; it's an industrial zone and maybe not all that safe for randoms during business hours. Plus it makes sense as general security for tenants in the zone. This situation is not going to change.
On the other hand, the road is in really nice shape; I wouldn't be surprised to find out that it was paved by the municipality, meaning that the public should have the right to use it. It would certainly make sense to put in a bike-width gate, and perhaps have it open just on week-ends.
Biking-wise this stretch of the Mon is just a dotted line (along the shore) on some planning document. I don't see anything happening in the next few years, at the very soonest. Why wait? Opening 2nd avenue would immediately make a significant improvement to the local bike path system.
So, actually, has anyone looked into this? Does anyone know where to ask or who to talk to? I'm happy to get it started if someone points me in the right direction.