You can do this with a microflow that performs a change action on your entity and set the desired date time field with the current date time token. The token can be found when using the generate button when setting the field that needs to be changed.
Hi Rhys, like Erwin said you can use the [%CurrentDateTime%] token. See this link for more tokens which you can use.
Thanks tremendously, I don't know why I never saw that.