Here are the arguments of afterlife according to Quran:

1- Just as our Creator gave us life in this world He will bring us back to life on the Day of Resurrection.

2- Allah Who created the heavens and the earth and was not tired of it can easily bring the dead back to life.

3-Allah Who created the heavens and the earth can create the like of them. He can create the Hell and the Paradise.

4- It is He Who originates the creation, then will repeat it and it is easier for Him. As doing the same for the second time is naturally easier than the first time. Although neither the first nor the second creation is difficult for Him.

5-Afterlife is the natural demand of our morality as we know that good and bad are not equal and same and they shouldn't be. Should the reward of prophets and pious people (who are the best people of humanity) and the worst people be the same. Should human beings and trees or insects be dealt equally that both die and that is all?

Here are some verses from Quran having such arguments.

(Al Kahaf Sura No 18, Verse no 37)

Do you disbelieve in Him Who created you from dust, then from a sperm-drop, then He fashioned you into a perfect man?

(Al Dukhan Sura No 44, Verse no 38)

And We have not created the heavens and the earth and all that is between them for amusement.

(Al Maryam Sura No 19, Verse no 66-67)

And man (the disbeliever) says: "What! When I am dead, shall I then be raised up alive?" Doesn't he remember that We created him before, when he was nothing

(Yaseen Sura No 36, Verse no 77-83)

Does not man see that We created him from a mere sperm-drop? Yet behold! he (stands forth) as an open quarreler. And he makes comparisons for Us and forgets his own creation. He says: "Who will give life to these bones after they are rotten and have become dust?" Say: "He will give them life Who created them for the first time! And He is the All-knower of every creation!" He Who produces for you fire out of the green tree, when behold, you kindle from it. Is not He Who created the heavens and the earth, Able to create the like of them? Yes, indeed! He is the All-Knowing Supreme Creator. Verily, His command, when He intends a thing, is only that He says to it, "Be" ــ and it is! So glory to Him in Whose hands is the dominion of all things: and to Him will you be brought back.