can I open the door on Shabbos if I see my order about to be delivered to my house
by the UPS driver?
My understanding of your question is that you want to know if you are allowed to ask or let the UPS driver place the package inside your house, which means that he is carrying the package for you from outside the house into you house. It depends on the circumstances, and not all cases are the same.
If your house has an eruv around it, or a porch which would make it into a reshus hayachid, (a private domain), then you aren’t really asking the driver to do any melacha for you. It is his responsibility to carry it until your front door, and he is paid by UPS to do that, and once it is already in your reshus, asking him to carry it another two feet, is only asking the gentile to carry muktza, which is permitted.
If however your house is up against the street, then essentially you are asking the driver to carry it from a reshus horabim (public domain) or karmilus (technically not a halachic public domain, but similar to it, and subject to Rabbinic prohibition to carry in that area), then it is more complicated. Then it depends if the driver is performing an issur d’orayso (carrying from a public domain to a private one) or d’rabonon (karmilus to reshus hayachid), by bringing it into the house, and the reason why you want him to bring it inside. If the reason is only for convenience sake, then you shouldn’t ask him to bring it in because we don’t ask a gentile to do melacha for us even if it is only a d’rabonon. However if the reason you are asking him, (or hinting to him) is because you are afraid that the package will get stolen if it is left outside, then we might have the rule of “shvus dshvus bmakom hefsed”. We are allowed to ask a gentile to do a melacha d’rabonon for us if it is in in order to prevent a loss. If the action of the driver would be classified as a d’orayso, i.e. you live on a main road, which can be classified as a real reshus horabim, and the driver took the package out of the truck, put it down in the street, then picked it up and placed it inside you house, then since he did a melacha d’orayso, you wouldn’t be able to tell him to do it. (If he carried the package straight from the truck to your house without stopping it would also be rendered d’rabonon and permitted). However, if you live on a street that isn’t classified as a real reshus horabim, then it would be permitted to ask him to bring it in, in order to avoid a loss.