Connecting flight in San Jose
 

If I arrive from the U.S. at 2:30 PM would it be possible to catch a nature air flight one hour later or is that cutting it way too close?

Not possible at all. Nature Air uses a different airport about 30 minutes away, although it has transferred some of its operations to the international airport where you'll arrive. Even if you have one of those same-airport flights, you have the general hubbub of disembarking from the plane, immigration, baggage claim, and customs to deal with. There's no baggage transfer or issuing of boarding passes between the international airlines and Nature Air. You will have to check in again.

Did you take a look at Sansa at all? They may go to the area you're interested in and are located right next to SJO and may have times that suit you better. Agree with Jeff, no way you can make that Nature Air flight.

Even Sansa being next door, I'd never trust any time so short to make a flight.

Sansa may offer different times though that work with their schedule.