"Time" with the definite article would signify a specific time, as in,
Do you remember the time when we were so poor we had to eat ramen?
or Michael Jackson's famous song:
Do you remember the time
When we fell in love
Do you remember the time
When we first met, girl
Even if "the time" is not followed by "when.....", it will normally be specified elsewhere in the text, or the speaker will allude to a specific time that the person s/he is speaking to would remember.
Those were the times!
is a phrase that would be used when someone is being nostalgic, after mentioning which time(s) exactly that was/were (college years, or else).
Another option:
I could have baked three cakes in the time it took you to bake just one!
Here again, "the time" is defined as that specific stretch of time in which this person baked a cake.
Your examples just refer to the general passage of time, not to specific stretches of it. So no article is necessary.