The OED’s second definition of infinite is, when it is used with a plural noun:
unlimited or indefinitely great in number; innumerable, very many, “no
There this supporting citation with ways from 1775:
Thus there are . . . infinite ways of being vicious, though but one of being
However, the entry describes this use as being now archaic or rare. It is probably best avoided for that reason and because, as the other answers show, its use is controversial.
In the example, an infinite number of ways is preceded by There are rather than There is because an infinite number of premodifies the plural ways. This contrasts with the infinite number of ways, where singular number is the head of the noun phrase and so would require singular agreement.