In general, you should have few problems withdrawing cash if you're not in middle-of-nowhere. Most Seven Bank, AEON Bank, Lawson Bank and "big four bank" (Mitsubishi UFJ, Mitsui-Sumitomo, Mizuho and Resona) ATMs (or, in case of ATM booths, they usually will have at least one ATM that) support international withdrawals, and MasterCard is surely not a problem given its universal presence. Even ATMs of smaller banks (e.g., some Bank of Yokohama and Ogaki Kyoritsu Bank ATMs) will allow international withdrawals.
If you're in any city of considerable size (definitely in Tokyo, Nagoya and Osaka, but even in Gifu or Matsuyama), you shouldn't have too much trouble finding at least a Seven Bank ATM which accepts your MasterCard: that would usually be in a Seven-Eleven, of course, but you'd have good chance of finding one at a (larger) train station or a subway station. FamilyMarts and Lawsons usually have ATMs too, which will probably accept international debit cards.
No need to worry too much about the cash withdrawal situation. That said, you're better off withdrawing as much as you can at once, to get lower effective international transaction fee rates. You may also consult if your bank has an agreement with a Japanese bank (likely one of the "big four") to save on transaction fees.