Hill, who recently earned his place on the world snooker tour with a win at Q School, made a fine start to his 2022/23 campaign.
The 20-year-old Irishman kicked off the day with a 3-0 thrashing of Craig Steadman, before holding David Grace and Ben Hancorn to 2-2 draws.
Hill finished his group with the same number of points as Grace, but edged the Leeds-player on frame difference to finish top and seal his place in the second stage.
Finishing top also earned Hill £3,000, while second-placed Grace took home £2,000. Hancorn finished in third spot to claim £1,000, while Steadman left Leicester's Morningside Arena empty-handed.
In the other group, it was England's Milkins who progressed in the Championship League.
The player whitewashed Sanderson Lam 3-0 before beating Allan Taylor 3-1. In the final game, he held former crucible semi-finalist Andy Hicks to a 2-2 draw.
That final result proved crucial as Milkins edged Hicks on frame difference to finish top of the group, earn £3,000 and secure his place in the second stage of the tournament.
Hicks had to settle for second and £2,000, while Sanderson Lam sealed third-place with a 3-1 win over Allan Taylor to take home £1,000.
Wednesday's action will see two more groups, with the first featuring Zhao XIngtong, Hammad Miah, Adam Duffy and Michael Holt.
The second group will include Noppon Saengkham, Anthony Hamilton, Ashley Hugill and Steven Hallworth.