The 57M is a lever-matic produced 1959-69. Only a little over 22,000 were made.
I had thought MAYBE it was chambered for .22 WRF, which is a shorter case than the WRM. But Marlin never produced any chamberings for the WRF.
I don't have a 22 mag tube feed so don't know how long the feed slot should be. My Model 60 (LR) has a feed slot about 1 1/8". It would appear that the tube has been changed and the wrong one used. Winchester .22 mag along with all other brands are the same OAL....or very close. If it wont feed in the slot I suspect none will.
Solution is to obtain the correct feed tube. But unless you want a completely correct part gun I would remove the inner tube and feed the shells into the end of the tube. See if the gun will cycle and function. If so simply enlarge the feed slot. This can be done with a Dremel tool or file. I would remove the tube to perform this so as not to get any filings into the tube that will get into the feed portion of the gun. Clean the tube thoroughly before assembly. If you don't feel comfortable in doing this then have a Gun Smith do it.
Only question is will the gun function correctly without the correct feed tube. That's why I would insert the rounds into the end of the tube first to check. I checked Brownells and they do not list a replacement feed tube for the 57M. Marlin did produce a Model 57 which was chambered for .22LR. If the tube has been replaced it may be a tube for a standard model 57.
Tube feeds often was the first thing to get damaged on these type of guns. Bent, dented, ect. Having to replace one is not uncommon. Another concern would be is the Inner tube correct. Both the Inner and Outer tube must match for the feed to work correctly. Again this can be checked by inserting rounds into the tube without the inner tube, insert it and see if the gun cycles OK.
The 57M Lever-Matic is a fine gun and hope you correct the feed problem. Please let us know how it goes.