Also heavy Ankle Slicer or Triple Axe reaches quite far, so in many cases you can sneak these in once you’re in range depending on what your opponent is gonna try next to keep you out. In the case of Shago and Omen they’re likely to go for the slide (often) and Ankle Slicer crushes low attacks (completely beats them).
Otherwise, when you pick a grappler style character you’re signing an unwritten agreement that this is your future vs zoner type characters:
As others have said you just have to put up with it and walk forward carefully until you’re in smashing range.
In terms of Thunder, you also have Call of Sky at your disposal (PPP) which charges his next dash to become an instinct dash, which will aid you in moving through a problem attack to get closer to the opposition. (not super great against Kilgore, though)