The 25-year-old Brazilian attacking midfielder signed for a reported £33.5 million from Lazio on Sunday.
England, set 257 to win, finished on 260 for two, with Test skipper Joe Root 100 not out on his Yorkshire home ground.
Van Avermaet leads Thomas, in second, by 2min 22secs, with Alejandro Valverde now up to third at 3:10.
The US finished with a final tally of 219 points while Poland came second on 162.
The modified route to run between Astrakhan and Moscow from July 21 to 27.
The Canadian will next face 2016 Gstaad champion Victorija Golubic.