Could Puck's jests about the irony of the situation be referring to Lysander, Helena and Hermia's childhood together?
Some of the text in scene 1 seem to hint at Hermia, Helena and Lysander having a childhood together. Puck often jests toward the situation having irony.
I don't think so, no. You're absolutely right that Hermia and Helena (we're not told about Lysander and Demetrius) have known each other since they were children, and went to school together.
But I don't see that history - which is definitely in the text - reflected in what Puck says to taunt them.
Captain of our fairy band,
Helena is here at hand;
And the youth, mistook by me,
Pleading for a lover's fee.
Shall we their fond pageant see?
Lord, what fools these mortals be!
Puck thinks it's funny that Helena is here - and the wrong youth (i.e. Lysander, who Puck has anointed with the flower!). He laughs at the felicity of the situation: that the lovers have all coincidentally arrived at the same place.
Then will two at once woo one;
That must needs be sport alone;
And those things do best please me
That befal preposterously.
Puck just enjoys the trouble of the whole thing!
Believe me, king of shadows, I mistook.
Did not you tell me I should know the man
By the Athenian garment be had on?
And so far blameless proves my enterprise,
That I have 'nointed an Athenian's eyes;
And so far am I glad it so did sort
As this their jangling I esteem a sport.
Again, Puck there is reiterating how much it's "sport" (fun) to him to see the lovers "jangle" and fall out with each other. It's a happy coincidence that they all arrive in the same part of the wood. Perhaps the trouble and the assumed betrayal of Hermia by Helena is worsened by the fact that they went to school together and knew each other when they were young. But I can't find the irony or the references to their childhood that you imply in your question.
Hope it helps!