Hello Tim,
Welcome to Microsoft Q&A.
Judging from your description of the problem, even if you physically connected the keyboard to the Surface Pro 11 before turning on the Surface, the keyboard still couldn't be used when you pressed the power button to start the Surface, right?
At this point, please find the Surface App in your Surface Pro 11. It is usually pre-installed in Surface. If you don't see it, you can also download it directly from the Microsoft Store. After opening the Surface App, please confirm whether you can see your Surface keyboard here.
If you can't see the keyboard at this moment and can only see it after removing it and reconnecting it, then I guess the problem might stem from the driver or the firmware. After all, this is a newly bought Surface, and perhaps the driver and firmware need to be updated. Please visit the following support link to manually download the driver and firmware package that is compatible with your device model:
Download drivers and firmware for Surface - Microsoft Support
Please be sure to choose according to the CPU model equipped on your Surface Pro 11, because the Surface Pro 11 has two versions. One is equipped with a Snapdragon CPU, which belongs to the ARM version, and the other is equipped with an Intel CPU:
After the download is complete, install it manually. Then, restart your Surface and check again to see if this issue will occur.
Best Regards,
Kai Ho | Microsoft Q&A Support Specialist