With Jira by itself, no, it's not currently possible.
But I did find an interesting guide on how you can limit the input of worklog dates to only 10 days in the past. It seems reasonable that you could modify this to be a much shorter range, such as 1 or even 0 days in the past.
However I believe for this to work, you would first need the Jira Workflow Toolbox plugin, and from there you could try to follow this guide: Limit Past Date for Current Work Logs.
I have not tried to do this myself, but I think it could work. Granted it probably would be complicated to set this up on all the transitions possible in all the workflows where you want to do this. So, it probably is not a simply fix, but it appears to have possibilities.
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