Just like how you can start a tween, wait, pause, and resume the tween at a later time, you should be able to start a tween as if some of the progress has already elapsed. For instance, as an argument to Tween:Play() which would be a number between 1 and 0, which is how much of the tween to “skip” before playing the rest, and the default value would be zero. Alternatively, there could be a Tween:SetProgress() which sets the progress variables to a given point immediately.
An example use case for this is, if I have each client play a long-running tween, I can more easily synchronize them if the players join at different times, for example, by using workspace:GetServerTimeNow().
Hey, not to be a prick, but if you want this to have a higher chance of being accepted, consider editing your post to be more in-line with How to post a Feature Request - Feature Requests; specifically, I noticed your post lacks the following:
Use cases. How do you intend to use this? (this is actually noted as required in the post I linked)
What are you not currently able to do (or what is too hard to do) without this?
What problem did you face that led you to make this?
That works when you’re trying to do more complicated/advanced tweening, but for such a simple use case like this it should really be possible to do this natively within the Tween itself.