That's what I am so afraid of. The delivery guys in my current area are not even polite, it would be so difficult to make them stay while I complete the checks
One thing we could do is, to possibly have another person (family/friend) with us during the delivery, and have them take a video from the point the delivery person begins to open the delivery package, up until the time they leave our house. While the delivery person is still there, we might as well request them to wait for a few minutes, so that we could do a few verifications.
As it has been rightly pointed out earlier, the delivery person might not want to wait until we do #5 & #6 below. That's one of the reasons for taking a video. At least we could have on record (that they refused to stay for verifying these things), in case a dispute arises with Flipkart or Amazon.
Before Unboxing:
1) Make sure that the video captures our name & address on the delivery package.
2) Confirm that the seal on the phone's box has not been tampered with. If the seal is already broken, it could very well mean that it could be a refurbished phone (or even a damaged phone with something like display or software issues). In such a case, we could then choose to refuse to accept the delivery.
3) Make sure that the video captures the IMEI on the phone's box.
After Unboxing:
4) Check the phone for physical damages & screen scratches.
5) Turn the phone on and confirm that the IMEI on the phone's box matches with the IMEI displayed on the phone.
6) Register the phone on the manufacturer's website/app & verify the warranty period. We can try to create an account on their website/app as soon as the new phone is shipped, and keep it logged in before the delivery (using another phone or pc). This way, we could enter the IMEI & other details as quickly as possible & try to register the phone quickly.
I did have a video taken by someone when I unboxed the last phone that I received from Amazon. This was not an open box delivery & so I unboxed it myself. Thankfully, nothing turned out to be out of the ordinary.