This isn't necessarily true; the
contents of the universe are timelike, but the universe itself may not be.
Neither of these are necessarily true - the first assumes absolute time, which we know from General Relativity to be incorrect; and the second assumes the low entropy state at the big bang is a one-off, which isn't necessarily true. Both General Relativity and quantum mechanics (and combinations of the two) have solutions that allow infinite past and future temporal extents (here's
a recent QM based hypothesis that doesn't involve eternal past entropy increase). There are also so-called 'closed' models where spacetime 'folds' round at the big bang so that time itself begins within the universe, but the universe itself is timeless, i.e. it just
is. Another interesting one is
a time-symmetric universe expanding forwards and backwards in time from the big bang.