I'm more than happy to be proved wrong, but having gone back through the ESA legislation this afternoon I can see nothing that allows the payment of ESA prior to the Commencement of the award.
There is one specific circumstance where what you are asking would be allowed, which is that you backdated your ESA claim to include the period of EPS, so the Commencement Date includes the EPS, but your post suggests that this was not done and I don't think there is any way that you can respectively change the start date of your claim.
However, you lose nothing by trying. ESA claims can be backdated by a maximum of 3 months providing the period is covered by a Fit Note.
Gordon
Gordon
Nothing on this board constitutes legal advice - always consult a professional about specific problems