I am pretty sure this has already been proven wrong. Please give credit where credit is due. If it weren't for operation Warp Speed [1] and the millions of doses bought under the Trump administration, Biden wouldn't have anything to take the credit for [2]. CNN neglected to credit the Trump administration for this. Yes, his (Trump's) handling of the crisis was awful but it doesn't help to lie.
It's likely quite true that the Biden administration has increased the speed of vaccination, with Warp Speed providing the base they built from. Hard to make a concrete argument about how much difference, but I think the direction is obvious enough.