After having the oil changed and driving home I discovered the oil filter was loose, engine will not start

Hello,

If there is no oil in the engine and you try to start it, it can get seized.
Have you contacted the oil change place?
As it is their responsibility to get this take care of for you.
Typically shops have insurance coverage for this types of mishaps.

When an engine is seized it could do severe damage to the internals and many times the engine might need to be rebuilt.

https://www.2carpros.com/articles/how-a-car-engine-works

Let me know if you have any questions or concerns.

Thank you.

It does have a oil pressure sensor, which could trigger the no start due to not sensing oil pressure. It will send a signal to the computer of no pressure and the computer will not allow the engine to start.
The biggest issue is when an engine gets started with no or very low oil the internal friction of the engine components will create hot spots and could lead to severe damage. And you won't know what the damage is unless the engine gets taken apart.

It will depend on the error code that got generated by the sensor. Might have to clear the code before trying to start it again, after you add oil.

https://www.2carpros.com/articles/checking-a-service-engine-soon-or-check-engine-light-on-or-flashing

Just keep in mind there could be internal damages due to the start with no/low oil.
And if the engine is seized it will not start regardless of the sensor.

You're welcome.
Let me know how it turns out.