Depends on the language honestly. In my native language (that’s not English) it sounds somewhat clumsy with the zero in front, but it’s still sometimes used. Depending on the context it might be a simple number (zero two) or it might be an ordinal (zero second). From 2010 and on it’s been easier because you just say the equivalent of “tenth”, “eleventh” and so on.

In writing it also depends on the context - if it’s something ambiguous (that could be 1925 or 2025), then sure, write the full year, otherwise two digits are fine.