Will Godox TT350o work with Olympus EM10 M2?
Yes, the TT350-O is compatible with your camera body. The Godox website lists the following camera bodies on their compatibility list:
Olympus: E-M10 II, E-M5 II, E-M1, E-PL8, E-PL7, E-PL6, E-PL5, E-P5, E-P3, PEN-F.
Panasonic: DMC-GX85, DMC-G7, DMC-GF1, DMC-LX100, DMC-G85
In addition, the Flash Havoc blog has a comment from its author, elv, who states that this list of compatible bodies is merely what Godox has been able to test the flash against. I own a Panasonic DMC-GX7, and my TT350-O works fine in all functions (HSS, TTL, MULTI, S1/S2, 2nd curtain, etc.) on the camera's hotshoe.
I also have no idea what you mean about the flash being "not that small". It's tiny for a speedlight with a tilt/swivel head! Godox gives the WxHxD in millimeters (140x62x38). That's 5.5"x2.4"x1.5"--i.e., about the same foot print as a 3x5 index card. I find it to be the perfect size/weight for a mirrorless body.