Golem

A double earth golem is not as good as a double earth Rhydon, so I would TM to double rock.

Personally I would. With the exception of legacy Omastar, Golem is the only other viable Pokemon with double rock type moves.

A moveset update is speculated, and other Pokemon may get rock moves for example Rhydon or Tyranitar which would become better rock attackers than Golem, but there is no guarantee that they will.

On the other hand Golem may also get new rock moves and the best moveset on it may require a legacy move.

I think the safer option is to give it rock moves, because even if Rhydon and/or Tyranitar do get a rock quick move, and Golem is no longer the best rock-type attacker, it's still going to be a good one and so you won't feel like your TMs were wasted, but if Golem has it's best moveset become legacy you're going to regret not TMing a perfect one.

If you've decided that you are going to power it up, then yes you should TM to double rock. Double rock Golem is really the only Golem worth investing in.

If you don't have 6 double rock golems, using TMs makes sense. If you don't have 6 double ground Rhydons, you will get some use from it with ground moves. It is only the second best ground attacker, but the best rock attacker.
Yes, no, or later are all perfectly fine answers. Decide what you need for what you are going to fight.