It isn't really clear exactly what 'All of something that passes' means. Nor is it obvious that time is something that passes. Distance isn't defined as 'something that passes'; I am not convinced that time can be either.
Everything in our direct experience moves through time at a near constant rate; but then, everything in our direct experience accelerates towards the centre of the Earth at a near constant rate too. We need to be wary of extrapolating from local conditions to assumed universal constants; And phenomena such as
time dilation suggest that the constancy of our passage through time is a local, rather than universal phenomenon.
If time is a dimension directly analogous to but orthogonal to the three dimensions of space, as I suspect it might be, then there is no more a problem with the present being our current position in potentially infinite time than there is with here being our current position in potentially infinite space.