To clear up this freeze thing once and for all, there are various freezes of differing lengths. The pre-command freeze on type is one year, and to a different type it is four. When you first join, you also have an initial engagement freeze of five years. There is also another freeze which applies to new type ratings, which is six years.
Obviously they may release freezes as they see fit, but to keep things fair, freeze releases are typically done in seniority order, certainly within a fleet, and if possible across all fleets. So if you are junior and hoping to be released from a freeze, you need senior people to not want the course you are bidding for.
So when you first join, you have an initial engagement freeze (5 years), a pre-command freeze (1 year for on type and 4 years for a new type), and also a type rating freeze (6 years - I am assuming this freeze applies to new entrants, as it applies to all other pilots’ type rating courses these days, but this is a relatively recent extension from the old 5, so I am not totally sure whether new joiners are excluded from this freeze or not).
The consequence of seniority, means that for new joiners, the only freeze you are likely to be released from, is your initial engagement freeze, and overwhelmingly, this is most likely to be a move for a short haul command (due to you requiring the seniority for the move too).
So if you want the quickest short haul command, short haul FOs are currently getting to switch seats once their one year pre-command freeze is up and they have satisfied the experience requirements. If you start on a long haul fleet, you can expect to be held to your four year pre-command freeze (just as everyone on short haul is - it’s just that theirs is shorter because they are already on type). The only way you will move before four training years are up, is if all initial engagement freezes have been released, and they still have short haul command spaces to be filled, and I personally, would work on this being a highly unlikely scenario.