Do.

English 'do' is said to descend from PIE *dheH1 (so EIEC). The
PIE sense is 'put', 'set'.

Similarly, we are taught that the Germanic weak verbs are formed on a
post-positive form of 'did', 'I sleep-did', = I slept.

So. The first question.

Is this peculiar use of 'do' evidence for the (presumptively
non-IE) Germanic substratum? When you think about it, it really is an
easy 'creole-style' way for forming/adopting verbs; you can almost
hear pre-proto-Germanic-speakers fumbling around for a way to inflect
non-native verbs in a proper IE (ablaut-ridden) manner. Humm; how many
of the 'non-IE' Germanic substrate words are verbs?

The second question is the evolution into an auxiliary verb.

The idea of 'put', 'set' is pretty intense. 'Put' is rather
spectacular as a verb, in that it always requires an indirect object.
'Set' is almost as strong. Do-support in English did not fully
organize itself until after Shakespeare. One wonders why English
waited so long, or rather, why English needed to do do-support at all.

The real question:

Why 'do'?