My question is ...
When I was your age, the only thing I could think of is cricket.
Is this sentence grammatically acceptable under any circumstances?
Although, at first, is appears to be the problem, it's not; it's could. Here are two non-past uses of could, and neither fits the pattern you want,
To express conditional possibility or ability:
EX: You could do it if you tried.
In offering suggestions or advice:
You could write and ask for more information.
In short, given 'could think', we expect 'was', not is.