We can not prove it to you (i.e. convince you) if your mind is already set, but we can refer you to the evidence, then guidance is upon Allah to give. Stack Exchange is not meant for preaching and debating, so if you seek that you are in the wrong place.
The evidence that 'Isa is alive is in the Quran in three places. The first ayah is:
وَيُكَلِّمُ ٱلنَّاسَ فِى ٱلْمَهْدِ وَكَهْلًا
He will speak to the people in the cradle and in maturity (3:46)
This part of Surat Ale-Imran tells of the many merits, signs and specialties of 'Isa. Speaking to the people while still in the cradle is undoubtedly an extraordinary event and this happened as recorded in Surah Maryam (19:29)
The second miracle is 'speaking at maturity' (كَهْلًا) and this is pointing towards his address on his return from the heavens. This is the most plausible interpretation as otherwise speaking at maturity is normal and very unremarkable, it is not worth being mentioned in this context.
The second ayah is from Surat An-Nisa:
وَإِن مِّنْ أَهْلِ ٱلْكِتَـٰبِ إِلَّا لَيُؤْمِنَنَّ بِهِۦ قَبْلَ
مَوْتِهِۦ وَيَوْمَ ٱلْقِيَـٰمَةِ يَكُونُ عَلَيْهِمْ شَهِيدًا
And there is none from the People of the Scripture but that he will
surely believe in Jesus before his death. And on the Day of
Resurrection he will be against them a witness. (4:159)
The most plausible interpretation of "before his death" (قَبْلَ مَوْتِهِ) is before the death of 'Isa. Any other interpretation of the pronouns will be strange and easily disproved by simple observation, as we don't find them believing in 'Isa before dying themselves, and we don't find them believing in anything correct untill now, so the only plausible interpretation is that this will happen in the future, and 'Isa will only die after it will happen.
The third ayah is:
وَإِنَّهُۥ لَعِلْمٌ لِّلسَّاعَةِ
And indeed, Jesus will be [a sign for] knowledge of the Hour (43:61)
The most plausible interpretation is that "he \ it" (إِنَّهُۥ) refers to 'Isa, because the context both before and after this ayah is about him, it would be very strange to haphazardly change the subject to something that is not present in the context.
This ayah of Surat Az-Zukhruf tells that 'Isa will be a sign of the final hour. This means that he will come near it and hence that he is not dead.
Now, coming to your question. Your claim is that this ayah:
Muhammad is not but a messenger. [Other] messengers have passed on
before him. So if he was to die or be killed, would you turn back on
your heels [to unbelief]?
... says that the Messengers before Muhammad have died, so 'Isa must have died.
Your claim is false as قَدْ خَلَتْ مِن قَبْلِهِ ٱلرُّسُلُ does not literally mean that they have died, but means that "there have been" or "have gone". You can compare with ayat that use similar expressions:
مَّا ٱلْمَسِيحُ ٱبْنُ مَرْيَمَ إِلَّا رَسُولٌ قَدْ خَلَتْ مِن قَبْلِهِ
The Messiah, son of Mary, was not but a messenger; [other] messengers
have passed on before him. (5:75)
وَقَدْ خَلَتْ مِن قَبْلِهِمُ ٱلْمَثُلَـٰتُ
there has already occurred before them similar punishments (13:6)
Even if we were to accept for a moment that it is talking about death, there is no valid argument that ٱلرُّسُلُ means all the Messengers, as it can mean some (بعض). Consider these ayat:
وَإِذْ قَالَتِ ٱلْمَلَـٰٓئِكَةُ يَـٰمَرْيَمُ إِنَّ ٱللَّـهَ ٱصْطَفَىٰكِ وَطَهَّرَكِ وَٱصْطَفَىٰكِ عَلَىٰ نِسَآءِ ٱلْعَـٰلَمِينَ
And [mention] when the angels said, "O Mary, indeed Allah has chosen
you and purified you and chosen you above the women of the worlds. (3:42)
إِنَّ ٱلَّذِينَ تَوَفَّىٰهُمُ ٱلْمَلَـٰٓئِكَةُ ظَالِمِىٓ أَنفُسِهِمْ
Indeed, those whom the angels take [in death] while wronging
These ayat do not mean that all the angels came to Maryam, nor that all the angels take souls on death, but it means some angels.