None of my books indicate exactly when Smallwood's and Foreman's militia brigades first came into action, unfortunately. However, we do know that:-
(a) it was the first formation to march off when evening fell on the previous day (Oct. 3);
(b) it had the furthest to march - almost 20 miles into the centre of Germantown, 15 of them down the Lime Kiln Road and then Old York Road; and
(c) it came into action against the QRs and the flank companies of the Foot Guards, at around the same time that MacDougall's men were engaging the 1st Light Infantry (both formations accused the other of "bugging out" and leaving them to fight the British alone!).
The march would have taken them some 6 hours+ in good light, I would suggest half-speed (1-2 mph) in the darkness and fog. Some of the left flank column's scouts got lost, taking wrong turnings to left and right, and some were captured. To be honest, I don't think Smallwood's men did any fighting at all, and Foreman's only a little - most writing on Germantown don't even mention them (even when it does mention the right wing attack by the PA militia).
Based on when most of Greene's division got into action, which was some time after Sullivan's given how they blundered into Wayne's rear, my guess would be somewhere between 07:30 and 08:00, probably engaging their opponents (which later included the 27th and 28th Foot) for about 30 minutes, no more, and then retreating - possibly because their ammunition ran low, but I suspect that confusion and loss of officers may also have been responsible. Also, Smallwood's brigade may well be the same units that had run away in panic during the night march to support Wayne at Paoli (I'll check that).
If I find anything more definite I'll come back to you.