The iPhone Pro Max is roughly 16 cm tall and 7.8 cm wide. Any bag with an interior compartment longer than about 17 cm will take it lying flat; shorter than that and the phone stands up and pokes out the top. Here is how to pick without guessing.
The 17 cm Rule
Measure the bag's main pocket, not its outside. You want at least 17 cm of clear interior length and a depth that lets the phone lie flat. The colorblock crossbody clears this easily and still reads as a small, sharp daytime bag — proof you do not need a tote to carry a big phone.
Styles That Work
A structured crossbody with a full zip, a top-zip pouch, or a vertical mini bag all fit a Pro Max if the pocket is deep enough. Soft slouchy bags can swallow the phone and let it spin, so check the base width. The crossbody edit is the safest place to start because most are built for a phone-plus-cards everyday carry.
What to Skip
Pro tip: if a bag's only pocket is a slip pocket shorter than your phone, skip it — the phone will ride above the flap and either fall out or bulge the shape.
When in doubt, carry phone + cards + a lip balm and nothing else; that is the real "small bag" test. Pick from the crossbody collection and you will never juggle your phone in hand again.