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Is this normal? This way it seems I can’t do an SMC, because any press on a key will start up the MacBook Pro. How do I do an SMC on this MacBook Pro?

Wherever you are in the world you should just head to Applecare, either online or in a local store. What you are experiencing is not normal at all and will most probably lead to a Mac replacement.

This is normal. The Mac is designed to auto start when you press any key. Just hold down Shift+Option+Control when the laptop is off for 7 seconds. It will turn on. After 7 seconds keep holding the keys down and additionally press the power button (Touch ID). The laptop will turn off. Wait a few seconds then turn it on normally, and your SMC should be reset! See: https://support.apple.com/en-ca/HT201295