Goto button to week/day of first available slot for booking

is there a feature that let a user to go to first week where has bookable slots available. In this way the user does not have to page through a lot of empty pages (noSlots) but can reach first available with one click.

There is no ready way, but it is possible to implement.
The way depends on what you mean by “available bookable slots”. If you mean only slots without events (and this doesn’t connected with blocked slots), please try the next way:
take events from now until sometime in the future and check where the nearest empty time is. for example you can use getEvents() for it.