Can you connect to a mobile network without a SIM?
I know during emergency calls we can connect to our mobile networks without using a SIM and make calls. So it's technically possible to connect.
The SIM card holds encrypted info on how to authenticate to the mobile network.
So my question is: if we have access to the encrypted data of the SIM, would it be possible to connect to the mobile network without using the SIM, by manually entering the information on the device? Can this be done without an internet connection? Can this be done on an average phone?
From Wikipedia: SIM card:
Authentication key (Ki)
The Ki is a 128-bit value used in authenticating the SIMs ....
The SIM card is designed to prevent someone from getting the Ki by using the smart-card interface. Instead, the SIM card provides a function, Run GSM Algorithm, that the phone uses to pass data to the SIM card to be signed with the Ki. This, by design, makes using the SIM card mandatory unless the Ki can be extracted from the SIM card, or the carrier is willing to reveal the Ki ...
Thus, by design a SIM card (or something similar, like eSIM) is designed to be mandatory for authenticating against the network. There are some weaknesses (also described in Wikipedia) which might allow to extract Ki, but even then a SIM card with Ki inside would have been needed in the first place.
Emergency calls don't require authentication though. They only require identification of the device, which can be provided without SIM. But for anything which should be payed for the billing contact need to be known - which requires authentication. And since authentication is provided by the SIM it means that there need to be an associated SIM card or eSIM.
... would it be possible to connect to the mobile network without using the SIM, by manually entering the information on the device?
There are cryptographic operations done on the SIM based on the authentication key. It is not possible to just do these simply manually, but it can be done by software: a SIM card is basically software too, only on a protected hardware.
Can this be done on an average phone?
One would need to have deep access to the software stack of the phone for this. There is no interface for this on average phone.