any possible ways to implement "reliable bloom filter"?

I know bloom filters can help with checking if some element is in a set while saving considerable storage space compared to keeping every element in a container, like std::set, to search for.

I also understand that bloom filters are probabilistic data structure, where the accuracy, or the possibility of generating false positives, will converge to a math expression. I was wondering whether it is possible to find some kind of data structure that is as efficient as bloom filters in terms of storage space requirement, probably with some inevitable compromise in time complexity of searching, but at the same time deliver 100% positive judgment, which excludes any chance of false positives.

I checked out cuckoo filters and xor filters and came to realize that it seems impossible to find the answer out of bloom filters because of their probability nature. Is there any kind of data structure that satisfies my requirements? Or is this kind of data structure literally impossible to be implemented? Are there any more directions I can do further research in, and if so would you please name some keywords?

Sincere thanks for your patience!