Minato has to mark him with the tag. Shunshin requires chakra buildup. Minato does not have great base speed feats.
Edo Tobirama (who is not at 100% power) successively attacking Rinne rebirth Madara using FTG inspired by Minato and this Madara is consider as more powerful than Edo and EMS Madara even Hashirama admitted it. Safe to say this Madara also is stronger than Hashirama. But we saw how Edo Tobirama put a work on Madara using FTG V2. Edo Madara able to counter all Tobrama's attack bcus he has Sage Mode power plus all the body modifications advantages. Tobirama first strikes Madara using his trademark move, Hiraishingiri but Madara dodge the attack help by his Sage sensing. And what happen after that is offpanel.
But what I want to tell you is that 1) Rinne Madara is stronger than Hashirama 2) Tobirama in his prime is the fastest person in Madara's era, admitted by Madara himself. 3) Edo Tobirama gives Madara a hard time using FTG 4) Edo Tobirama acknowledge Minato's speed prowess and he said "Minato is faster than him" 5) Hashirama never started any battle using SM.
So try to connect the dot. How the battle start. Both Hashirama and Minato start in base. As its proven that Minato is faster than Tobirama (Shunshin wise) there is no reason to believe that Minato doesn't have great base speed as in two occasions it shows him travel in great speed (saving baby Minato and arriving to battlefield first before other Hokages). So in this battle Minato can speed blitz Hashirama easily. Or just shunshin to Hashirama and leave the FTG mark on him. If Edo Tobirama can surprise attack Rinne Madara using his foot speed why Minato couldnt do the same thing to a person that below Rinn Madara?
Therefore Minato can just speed blitz Hashirama from the start of the battle bcus he can without plot. Speed always trump strength.