JimG
Yeah, check fluid level first
I ran into this problem with my 3.0 E46 transmission with no transmission engagement in cold temps (neither drive nor reverse) until a very warmed up coolant temp.
Here is the thread on E46 fanatics.
https://forum.e46fanatics.com/showthread.php?t=893453
My problem went away when I replaced the solenoids in the thread.
These were my PNs and prices back in 2017 when I solved my issue in my 3.0 E46:
Main pressure regulator solenoid - AC Delco 10478146 Amazon Prime $36.00
Torque converter lock-up clutch solenoid - AC Delco 24227747 Amazon Prime $23.00
Here is another narrative with transmission info
Transmission Valve Body Removal & Installation, Filter, Fluid Service
Just a significant lowering of the valve body was necessary to swap out the solenoids.
My theory on why this symptom manifests itself is because the o-rings in the solenoids harden and shrink over the years and miles. This causes them not to function as designed until they warm up and become pliable and do their o-ring job
Mike