Hi Cozycamper,
If this is a quilted mattress pad that has compressed over the years then it could be affecting both the ability of the memory foam to soften with body heat and also interfering with the ability of the memory foam to compress with your weight. I would suggest taking this off and probably replacing it with a thin stretchy mattress protector which will have less effect on the mattress than this is probably having. A mattress pad like this can make a significant difference in some cases in how a mattress feels and performs … especially with memory foam. You may want to use a thin stretchy blanket for a few nights instead of this to see how much of a difference it may make.
I personally wouldn’t recommend memory foam for a newborn. You can read more about this and the various reasons why in post #2 here and the other forum threads it links to about mattresses, different materials, and children.
If I was adding a soft topper to mattress … I personally would make sure the materials were Oeko-Tex standard 100 class 1 certified (safe for babies). There are very few memory foam toppers that would have this certification in North America and I would tend to lean towards latex or natural fibers which have this certification.
If you do decide on memory foam … I would tend towards thinner layers (less risky for babies that can’t turn over and could sink into the memory foam). An example of a memory foam topper that is Oeko-Tex certified is here but even with it being “safe” … I would still tend to wait with a new memory foam topper until the baby was no longer sleeping on the mattress.
Phoenix