Start dates are anticipated to be allocated randomly between 13th May and 18th May. We believe there is, at the moment, no specific deadline for making claims for Self-assessment Income Support Scheme grants. You therefore have some time to make your claim and should not worry about this.
You should also note that some individuals who claim Universal Credit could be better off if they delay the claim so that the grant receipt falls into a later monthly assessment period. Universal Credit claims are complicated, but it is worth considering the impact of the grant claim on any claims you may be making.