What would it happen if there isn't a goal or behind and the ball doesn't go out of bounds? I mean a total clanger.
A Free Kick may be awarded when the football is or is not in play. For the avoidance of doubt, a Free Kick may be awarded:
(a) if an infringement occurs on the Playing Surface before the commencement of a quarter, in which case the Free Kick shall be taken at the Centre Circle or where the infringement occurred, whichever is the greater penalty against the offending Team
This has happened a few times in the AFL, and play continues as it would for any other free kick, as a centre bounce isn't strictly required to start a quarter. This isn't very explicit in the rules, but there is one fairly convenient "out" clause.
First off, the start of the match is defined as being when the siren goes to start the quarter, not when the ball is bounced. So if a player gives away a free kick in that time period, it doesn't matter that the ball hasn't yet been bounced, as the match is already underway and the free will be given.
As for the clock starting, although the rule of thumb is generally that time starts when the ball is bounced as per 10.5.2(b), there's two alternatives that can apply here:
10.5.2 Recommencing Time
The Timekeepers shall recommence the clock used for the timing of a Match when:
(a) directed to do so by the field Umpire in accordance with Law 10.5.3;
(e) the football is obviously in play;
I expect that the umpire would signal "time on" on giving a free kick before the centre bounce, but even if they didn't, the timekeeper is able to do it of their own accord because the football is clearly in play at that point.
At this stage the match is in the same state it would have been even if there was a centre bounce - the match has started, the ball is in play, and the timekeeper has started the clock.