I would not risk it. Please note there is always a small chance of a printed mistake being in your GC. ive heard of USCIS messing up middle names, DOB, expiration yrs, on which you must reach out to them to get it corrected before using it.

no wait until you get it, for your safety

Also, there has been instances where GCs are sent back to USCIS marked as undeliverable. Or could get lost in the mail & you would have to do the whole replacement process. Also, not sure what kind of GC it is, but be aware of USCIS asking for travel history when applying for citizenship, it would look weird if you left the country before the GC arrived.

while there are risks to everything in life, I did exactly what you just asked when I first got my green card … left the country after my green card had being created and being shipped .. a family member brought it to me in my home country as I had to travel urgently … however in my case I was not worried cos I came into the country with an immigrant visa and I know that is good for a year so technically I had my green card with me and just had to make sure if i did not receive the physical card for any reason listed above, I could travel still with that stamped visa serving as green card