Learn Polish: Nie zdążyliśmy tego kupić, bo ludzie wszystko błyskawicznie wykupili. - We didn't manage to buy this, because people instantly bought everything up.

Both verbs are perfective, but the prefix wy- adds the meaning of exhausting or fully depleting a supply. While kupić is just the completed action of buying, wykupić means to buy up the entire stock until absolutely nothing is left.

Why is it tego kupić (genitive) instead of to kupić (accusative), since the negated verb is zdążyliśmy?

This is a classic Polish grammar quirk called genitive climbing. When an infinitive like kupić is paired with a negated phase verb like nie zdążyliśmy, the direct object of the infinitive changes to the genitive case. The negation essentially reaches through the first verb to affect the object of the second verb.

Is there a reason we use the perfective zdążyliśmy here?

The verb zdążyć means to manage to do something in time. Because the speakers are talking about one specific, failed attempt to beat the crowd, the perfective aspect is required. You will rarely see its imperfective counterpart zdążać used this way, as that mostly implies a repeated habit or physically heading toward a destination.

What is the root of the adverb błyskawicznie?

It comes from the noun błyskawica, which means lightning. So when people buy things błyskawicznie, they are doing it instantly, with lightning speed.