If we are going to drone on constantly about existentialism, it pays to examine the big question in relation to the subject—does objective truth exist? If it does, then existentialism is a moot point. All that must be done I accept the objective truth. If objective truth does not exist—or, more likely, we cannot find it—then existentialism is worthy of some thought.
The issue is if objective truth exists, we cannot find it because we are all experiencing everything subjectively. But to say that all things are subjective is to establish an objective truth. In terms you are likely ore familiar with, to say that everything is relative is to state an absolute. The statement both confirms and contradicts itself simultaneously. We obviously reach the limit of thought there. For every truth established as either relative or absolute, an additional thought makes it the opposite. An argument about which is the correct view would be infinitely repetitive.
The bottom line is objective truth must obviously exist, because even if it does not, it would be objective truth that objective truth does not exist. It is another pesky case of a concept being both true and false simultaneously. Everything we believe to be true could be wrong. We just have faith that we are not wrong. This is not to say objective truth does not exist. It state merely that we may have misidentified it.