Is Big Bang Theory true like 1+1=2 is?

They are two very different things.

Big Bang Theory is still under extensive observational testing, and in practice this will never end. That's how science works. We are constantly looking for the flaws in any good idea.

Mathematics, however, is not science. It actually uncovers 'facts' that are eternal such as 1+1 = 2. Even so, there are starting to be problems with the very concept of a rigorous mathematical proof of any statement.

If you are looking for things that are true...be a mathematician. If you are looking for things that seem to reflect how the world is put together and operates...become a scientist. But always remember that scientists uncover rules and patterns that nature seems to follow most of the time. There can exist and sometimes are exceptions to these rules, and these exceptions when found cause scientists to build the next round of 'better' theories. We have to respect this process, and assume that what we understand right now is the best that we have until we can find the exceptions, document them, and then craft the replacement. So far, Big Bang Theory is the best idea we have. We have discovered no issues that are not successfully covered by it given how well we presently can measure the factors that define Big Bang cosmology.