An update was pushed just today for Sonic Mania! The guide below may not work anymore.

Launch the game once online and it should work.

Another patch that works during runtime (without editing any files) has been made by Kaldaien.

You can find SpecialK here[gitlab.com].

If you do not wish to use this (or for some reason can't), follow the guide below.
Otherwise, I recommend this method the most (due to file preservation).

If you know how, you can simply use the IPS patch[drive.google.com] made by shicky256

Otherwise, you can follow the guide if you feel more comfortable hex editing :)

Follow these steps to ignore the user login checks:

1. Make a copy of SonicMania.exe
   
2. Open SonicMania.exe in a hex editor
   
3. Go to 1CAABE
   
4. Overwrite the byte with: EB

Before the edit, it should read: 75 30
After the edit, it should read: EB 30

And that's it! You're done! Enjoy playing Sonic Mania offline! :)

Before anything, you need to have a hex editor. If you already have and know how to use a hex editor, skip this step.

Basically, you can get just about any hex editor, but what I used in this particular instance was HxD, which can be acquired here[mh-nexus.de]. I recommend simply getting the portable version.

In this specific hex editor, as well as most others, you can go around offsets by either double clicking in the lower left corner or simply using the Ctrl+G shortcut. An offset is usually a large number indicating the position in a file.
For this guide this will be 1CAABE.

Once the offset box opens, type this number in and click OK.

The cursor will be moved to a different position now; this is normal. You basically moved the cursor to that said offset in the SonicMania.exe.
The next 4 bytes after the cursor should read:

After you have done that, check what the status bar says - if it says "Overwrite", it's good. If it says "Insert", then click the insert key on your keyboard to change the status.

Once the status is on Overwrite, simply write EB in the place where the cursor was (it should be on that 75) and you're done!

If those 4 bytes after where the cursor was previously now read:
you're done!

Open the file menu, hit Save and you should be good to go!

Please, keep in mind this is NOT bypassing any shape or form of a security check. The user with the modified binaries still MUST OWN the original game. The Steam API still checks wether or not the user owns the game.

It seems like a simple configuration oversight by the developers and as such it has a simple fix to it. This really took me about 5 minutes to figure out.