I'd say September at the earliest.
Prem is scheduled to finish on 26th July, FA Cup final 1st August and the Champions League runs 7th August to 23rd August.
Presume there will then be a break but shorter than normal, they will at least need time to schedule fixtures as normal on the assumption that at some point fans will be let back in.
What happens next will spend on how likely we are to have crowds back and when. Is it financially viable for L1 and L2 to start behind closed doors. If not you've got an issue with keeping the season across all divisions in sync.