aside from other considerations, suppose everything is absolutely correct:
some cartridges are 'low riders', meaning the stylus cantilever is very close to the bottom of the cartridge body's underside.
thus a low rider bottom of it's cartridge body may still be in contact with the raised edge of the LP, UNTIL, as you describe, it 'moves in' a few grooves, thus no longer being 'pushed up' by the raised edge, (thus allowed to drop down properly into the groove).
i'e. I bought a Wayne's Auto perimeter ring, it's outer edge is thin, yet up a bit from the grooves. My cartridge body is unable to get low enough to play the beginning of the 1st track, until the cartridge body moves in enough to get down enough for the stylus to get into the groove properly. My Sumiko might work, it has a much larger space from the stylus tip to the underside of it's cartridge body, I guess I could call it a 'high rider'.