Is it possible that time is something we experience more or less steady but could have moments of large variations that we don't notice?

Time is relative. Hence why it's almost impossible to punch a fly. To the fly you look like you are moving in slow motion no matter how quick you are. Also isn't sleep a bit like time travel? Sleeping for 8 hours feels way shorter than 8 hours when you are awake. Or like when you are at work and are very busy the time goes much faster than if you are bored and have little to do.

Yes. Lots of people don't notice or understand that their metabolic rate affects their perception of how fast time seems to be passing.

Because we use TIME as a reference to observe other actions there is no process for identifying the flow of time.

Even if it went backwards there is no possible experiment, using time, that will measure the rate of flow of time.

We PRESUME that it moves inexorably onwards yet that is not a necessary part of anything.

Consider if time was going backwards.

So I wrote this answer today. When you asked the question it was yesterday.

Now even if time is going backwards yesterday is still before today.

So you conclude that you asked the question BEFORE I answered it.

Which is true enough if you use the time as a measure of order.

But we already said that time is moving backwards. Hence time is NOT a measure of order.

But what possible activity could identify this? None.

Time flows slower for a moving frame of reference and for a frame in a gravitational field.

Schrödinger has a cat.