Oh man, you're going to have fun with that. A Non-GMS TC57 device is going to be a nightmare managing since it will be caught between to management styles.

First, since it is a TC57 it is running a minimum of Android 8, if not Android 9 which means that it is completely incompatible with Android+ (DA) based management in SOTI, so you can rule that option out. 

Secondarily, since it is a Non-GMS device you can also completely rule out being able to take advantage of Android Enterprise. This means you can't use any of the standard DO enrollment methods (ZTE, DPC Identifier, QR, or NFC) since there are no GMS services on the device. You also won't be able to leverage OEMConfig since it is only distributed via Managed Play today and with no GMS there is obviously no Play Store either.

This leaves you really with only one option from my perspective and that would be DO based enrollment through StageNow. You'll have to avoid an enterprise binding and assigning MGPA accounts in your enrollment rule as well. I'm not even entirely sure this would even work, but it should on paper. The DO management API is actually part of the AOSP image so you should technically be able to leverage it. Even if you do get the device enrolled in this strategy I am sure you will find over time that many features and functionalities will not be supported because that is such a rare configuration to handle. 

Oh and, no to the Chromium piece. Try SOTI Surf. You'll have to distribute it directly to the device as a Package since you won't have Play Store.