I don't think there's anything official as yet but you can see the current paths (subject to change) on RTT at the moment by looking at somewhere like Edinburgh and applying a TOC filter for 'LD' (which appears to be East Coast Trains). From which you can construct at the likely timetable. For instance
here is the services for 16 July 2021 (note that these won't be running as the service isn't expected to start until the autumn/winter but the paths are in the industry system).
Which leads me onto an observation. One of the selling points of East Coast Trains was supposed to be an early arrival from London into Edinburgh. Originally I think they were aiming for pre-10am but so far they best they've got is 1010 arriving into Edinburgh having left Kings Cross at 0545. But I note that LNER from May 2022 are proposing to have an 0630 departure from London arriving into Edinburgh at 1034. Leave London forty-five minutes later (at a vaguely more civlised time!) and arrive only twenty-four minutes later than the East Coast Trains service would have. LNER having a prod at East Coast Trains hoped for market perhaps?
I mean 50p says that they were told at the time that something like this was likely so they shouldn't be able to claim surprise. Though I'm not saying that they won't try...