Could matter be infinite? Perpetual motion and Big Bang theory seem to allude that the universe can’t last forever because matter and energy are dispensed.
Is it plausible the Universe has infinite matter?
Yes.  Currently it is at least plausible that the universe is spatially flat.  If that is the case then, barring global topological weirdness, it is also spatially infinite.  That would mean it contains an infinite amount of matter.
Disclaimer. I don't know how large the uncertainties on spatial flatness currently are: if Wikipedia is to be trusted $\Omega = 1.00 \pm 0.02$ ($1$ being flat) based on data from WMAP and Planck.