The regression theorem state tomorrow expected purchasing power of money is dependent on the known yesterday's purchasing power of money.
The regression is not infinite because there must be a starting point.
For fiat money is when the fiat money was backed by gold; for gold is when it was for the first time exchanged to be used for an indirect exchange (the reason money exist is indirect exchange); for bitcoin was when two pizzas were exchange for 10K btc.
Why gold was exchanged for paper, goats for gold and pizza for Bitcoin is unimportant as praxeology deal not with the reasons of actions but with the consequences of actions.
It is infinite for money, that is, it has go go backwards to a point in time there was no money, only barter. You said it again in the quote just here. fiat -> gold backed money -> gold -> gold first time it was used in indirect exchange --> ...then you missed the necessary precondition for the regression theorem: gold exchanged in barter for its intrinsic value*). It is the only way (according to the regression theorem) there could be a previous gold value for the first indirect exchange.
*) There were probably other commodities before gold, but that is not the point here.
It is not infinite for money. We don't know how many exchange happened between the first use of gold as an indirect mean of exchange (aka money) and the moment fiat money was introduced (backed by gold) and then how many exchange happened between the time fiat money were backed by gold and when the backing stopped.
But it is not infinite time. Also a transaction require time, so we have a finite time divided by a finite period of time. It must give a finite number last time I checked math.
So there must be a finite number of transactions in human history where gold is involved.
So the regression can not go on infinity. It must have a starting point.
In case of gold is when gold was first acquire with barter to be used later for an indirect exchange. The reason it was exchanged and what was the value exchanged for it is irrelevant (because value is subjective to the two humans involved in the exchange and we can not know it). What is not subjective was the price (we can know it). Once there is a price, the market forces will move it up and down in consequence of supply and demand.
In the case of bitcoin the subjective values of 10k BTC could be zero for the guy paying with them two pizzas (from his point of view he was giving nothing for something). And the value of the two pizzas sold by the pizza maker could be zero (because he had two already cooked no one wanted - and even in this case he could have given something he valued nothing for something with an unknown value). But the exchange established a price level market forces could move up and down.