Damaged floor tiles

[Imreallytiredandanxioustoday]

So we've just had our kitchen doors replaced and swapped the fridge for an additional cupboard. However the side panels were cu into 2 of the tiles. I cannot be dealing with ripping the floor up but we can't leave the tiles with massive holes in.
What can I do. Is there flooring we can just put over the tiles? I have no ideas at all

Can you source two new tiles and just replace those two?
Buy a similar tile and insert a piece in each gap?
Fill and cleverly paint match and touch up the filler so it blends in then seal with cleat top coat?

I have seen a video of someone laying vinyl over tiles, but they had to fill and level all the grout lines first, so I would try one of the above options before having to do all that!

My mate was telling me you can fill
It and make it match. I might try that first.
Thank you