It sounds OK to me; you can say "Time passes." A "significant part of our life" is a chunk of time.
The only thing that bothers me about this sentence is the use of waiting. We spend much of our life waiting for Mr/Ms Right to come along; it's not time that does the waiting.
If you want to combine "part of our life" with "passes", I would change the rest of the sentence to "while we wait for..."