Engine not working on new layout

First would be to adjust the track.

A sixteenth of an inch is a fairly large bump.  As suggested, getting that fixed in some way is key.

I agree with what the others have posted.  Look carefully at the joints between sections of track.  If they're not 100% smooth you can expect problems; a deviation of 1/16" is too much.  Make sure the little copper "fingers" are touching each other, not bent, and not sticking up.

Also look at your table surface.  If screws or nails are sticking up or two pieces are joined at uneven heights, you have to smooth that out.  Drive in the screws, plane down the wood, etc.  Just like a real railroad, your right-of-way is important!

Thanks for the feedback. I will look into fixing the track. It’s just hard for me to understand since the older Lionel can navigate the same issue and much worse with no problem.

Locos differ in subtle things (whether the wheelsets are out of gauge and how much) and not so subtle things (weight) that affect tracking. It's actually not surprising that different locos perform differently on track that may be suboptimal in its smoothness of level.

@Jwyd something else that would be very helpful here is a video showing the problem, and also a few close-up still photos of the problematic section of track.

You didn't say whether your MTH starter set was steam or diesel.  The wheelbase of MTH's starter set 4-6-0's and 2-8-0's is longer than almost any postwar Lionel steam loco except maybe the Berkshire.  When the starter sets came out about 20 yrs ago, I was surprised that MTH included those locos, because generally the longer the wheelbase, the more fussy a steam loco will be about track geometry.  Frankly it's a lot to ask that these locos will navigate O31 flat-topped rail.

Good luck in troubleshooting your problem.  If you find the cause, please come back with an update so that others can benefit from your experience.