Welcome aboard!
Ran into this issue on my G35, and have heard it from other owners over the years. There are several possible causes, but it's smart to go through the list.
First, check for ECU codes. A cheap reader, coupled with an app like 'Torque' are perfect for this. Every car owner should have one!
Even if there's no CEL, there still may be a code. Dirty throttle body or a dirty MAF sensor can cause this issue - easy fix as well. Also, a failing temp sensor can cause hard starting when hot. Bad camshaft position sensors are a common cause, and they're probably due to be replaced anyway. Not terribly expensive.
Less-commonly, a bad coilpack or a problem with the coil or starter solenoid can cause this... but I'd encourage you to start with the easy stuff first.
Keep us posted - we're here to help!