What is the maximum Mach number for a titanium aircraft?
To give an answer, I first need to get answers to a few more questions:

First question: Which titanium alloy would you consider? The choice of alloy will impact the answer much more than the base metal of the selected alloy. Since strength at elevated temperature is the figure of merit here, consider the spread of values:



Strength of various Ti alloys over temperature (picture source)

Second question: Which cooling is available? Is the aircraft propelled by liquid hydrogen which has a massive heat capacity per kilogram of mass and needs to be heated before it is injected into the combustion chamber. Or do you run it on kerosene, which allows to dump much less heat into it? The answer will tell you how much cooler the structure can be than the air flowing around it is.

Third question: What wing loading is possible? This is driven by the range and payload requirements of the aircraft, and your question doesn't give any details on this. A higher wing loading will translate into a higher heat flow since the air density needs to be higher, so the cooling can be less effective.

Fourth question: Do you insist on an attached shock which produces much higher peak temperatures in parts of the structure, but less thermal load overall, or is a separated shock possible which increases drag and thermal load, but reduces peak loads considerably?

Depending on the answers to those questions, the possible flight Mach number can be anywhere between Mach 2 and Mach 5. If you allow for specialty materials for highest thermal loads and make only the inner structure from titanium, the Mach number can reach into double digits.