It's an assumption people a LOT smarter than you have thought about. Alan Turing proved that most problems can't be solved by algorithms. That was what Alan mathematically defined, that was so important. This isn't something that would have eluded scientists for generations to come; the proof was elegant for its time, but is very simple, mathematically.

If Turing was never born, the momentum that was built by World War 2 wouldn't have been halted. Going from the analog machines of the time, to digital machines was pioneered by Claude Shannon, not Alan Turing. Shannon's work on switchboards was the basis for expressing logical statements in a circuit. That was what bridged the gap from analog to digital, and sparked the information age.

Had Shannon not made his discoveries, computer science would have been more affected than if Turing hadn't. Even so, someone else would have figured it out within a few years.

Turing did mathematical work. He had little to do with modern digital computing. His theoretical work is unrelated to what you think of when you think about computers. Turing's work was largely philosophical and mathematical.