How to find out whether a PRNG works well for ANY seed or not

I'm trying to create an original pseudo-random number generator for some reason. The problem is, I don't know how to find out whether a PRNG works well for ANY seed or not.

TestU01 and dieharder can test a PRNG with a particular seed, however, can't find out whether it works well with ANY seed or not.

Is there a good way to do this? (experimentally, not theoretically, I hope)