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Engine is not shipped with synthetic oil, engine does not require synthetic oil, good old fashioned dyno oil is used for both.
Just make sure, the oil used meets or exceeds the GM spec as listed in the owner's manual. For the H3 it is GM Standard GM6094M, GM's synthetic oil standard is GM4718M, which exceeds GM6094M.
As for when to start using synthetic...you want to see some fights, bring this subject up in a meeting with some engine heads.
Many will say that synthetic is too slippery to allow the rings to set, therefore, run dyno for a few thousand miles, then switch to synthetic. Some will say it makes no difference due to the heat, friction from new rings against a cross-hatched cylinder wall, and synthetic will allow rings to seat.
GM does ship all Northstars, LS series engine (Corvettes) and most turbocharged engine (Cobalt/Saturn Redline, etc.) with synthetic right out of the plant and there appears to be no ring setting problems. (LS engine were noted in the past to burn oil, but that was fixed in later years with new designed rings.)
I changed to synthetic at 2000 miles for two reasons.
One, get that break-in oil out, and from then on, go with the oil light.
Two, I have more synthetic oil on the rack than most auto parts stores due to a two-for-one sale I came across a year ago while living in TN. So it cost me $15.00 (plus Mobil 1 filter) to put synthetic in the H3. If I had not had cases of this stuff, I would have used a good grade of regular dyno oil.
Only thing I caution against is making sure to run oil that meets or exceeds GM's requirement since the oil life system relies on this grade to correctly monitor the oil system. Using oil that does not meet or exceed this requirement will make the oil life system inaccurate.