All prophets came with message of Tawheed. What differed is the legislation(Sharia). Anyone who believed in the message of Tawheed and followed their respective prophets would be eligible to enter Jannah.

Below Hadith indicates Jannah will be occupied not only by the nation of Muhammed(ﷺ). Other nations as well will occupy.

The Prophet (ﷺ) said, "Allah will say (on the Day of Resurrection), 'O Adam.' Adam will reply, 'Labbaik wa Sa`daik', and all the good is in Your Hand.' Allah will say: 'Bring out the people of the fire.' Adam will say: 'O Allah! How many are the people of the Fire?' Allah will reply: 'From every one thousand, take out nine-hundred-and ninety-nine.' At that time children will become hoary headed, every pregnant female will have a miscarriage, and one will see mankind as drunken, yet they will not be drunken, but dreadful will be the Wrath of Allah." The companions of the Prophet (ﷺ) asked, "O Allah's Apostle! Who is that (excepted) one?" He said, "Rejoice with glad tidings; one person will be from you and one-thousand will be from Gog and Magog." The Prophet (ﷺ) further said, "By Him in Whose Hands my life is, hope that you will be one-fourth of the people of Paradise." We shouted, "Allahu Akbar!" He added, "I hope that you will be one-third of the people of Paradise." We shouted, "Allahu Akbar!" He said, "I hope that you will be half of the people of Paradise." We shouted, "Allahu Akbar!" He further said, "You (Muslims) (compared with non Muslims) are like a black hair in the skin of a white ox or like a white hair in the skin of a black ox (i.e. your number is very small as compared with theirs). Sahih al-Bukhari 3348

Ibn Abbas reported: The Messenger of Allah, peace and blessings be upon him, said, “I was shown the nations before me and one or two prophets would pass by with only a few followers, another would pass by with none at all. Then a large crowd of people passed in front of me and I said: Is this my nation? It was said: No, this is Moses and his people. Then it was said: Look at the horizon. Behold, there was a multitude of people filling the horizon. It was said to me: This is your nation from which seventy thousand will enter Paradise without reckoning.”

Source: Ṣaḥīḥ al-Bukhārī 5378, Ṣaḥīḥ Muslim 220

Islam existed from day one.

And Abraham instructed his sons [to do the same] and [so did] Jacob, [saying], "O my sons, indeed Allāh has chosen for you this religion, so do not die except while you are Muslims." Quran(2:132)

All prophets came with message of Tawheed. What differed is the legislation(Sharia). Anyone who believed in the message of Tawheed and followed their respective prophets would be eligible to enter Jannah.

Below Hadith indicates Jannah will be occupied not only by the nation of Muhammed(ﷺ). Other nations as well will occupy.

The Prophet (ﷺ) said, "Allah will say (on the Day of Resurrection), 'O Adam.' Adam will reply, 'Labbaik wa Sa`daik', and all the good is in Your Hand.' Allah will say: 'Bring out the people of the fire.' Adam will say: 'O Allah! How many are the people of the Fire?' Allah will reply: 'From every one thousand, take out nine-hundred-and ninety-nine.' At that time children will become hoary headed, every pregnant female will have a miscarriage, and one will see mankind as drunken, yet they will not be drunken, but dreadful will be the Wrath of Allah." The companions of the Prophet (ﷺ) asked, "O Allah's Apostle! Who is that (excepted) one?" He said, "Rejoice with glad tidings; one person will be from you and one-thousand will be from Gog and Magog." The Prophet (ﷺ) further said, "By Him in Whose Hands my life is, hope that you will be one-fourth of the people of Paradise." We shouted, "Allahu Akbar!" He added, "I hope that you will be one-third of the people of Paradise." We shouted, "Allahu Akbar!" He said, "I hope that you will be half of the people of Paradise." We shouted, "Allahu Akbar!" He further said, "You (Muslims) (compared with non Muslims) are like a black hair in the skin of a white ox or like a white hair in the skin of a black ox (i.e. your number is very small as compared with theirs). Sahih al-Bukhari 3348

Ibn Abbas reported: The Messenger of Allah, peace and blessings be upon him, said, “I was shown the nations before me and one or two prophets would pass by with only a few followers, another would pass by with none at all. Then a large crowd of people passed in front of me and I said: Is this my nation? It was said: No, this is Moses and his people. Then it was said: Look at the horizon. Behold, there was a multitude of people filling the horizon. It was said to me: This is your nation from which seventy thousand will enter Paradise without reckoning.”

Source: Ṣaḥīḥ al-Bukhārī 5378, Ṣaḥīḥ Muslim 220