I do not believe it is the only way now. Why would God invalidate his former covenants?
Because the teachings of the earlier faiths have been changed/corrupted/lost. With time, the message got forgotten or corrupted. So people started doing one or more of the below:
- worshipping other gods along with The One and Only True God
- making idols
- saying that God begot a son
- saying that certain people were incarnations of God
- rejecting belief in God altogether
- elevating the status of some prophets to divine
- rejecting or blaspheming some of the prophets
Whenever God's message got distorted by people, or forgotten, a new messenger was sent, not with any new or changed message, but reinforcing the actual message that God sent all the messengers with, the actual core beliefs that people were taught from the beginning of humanity, confirming the true parts of previous teachings and scriptures, and correcting wrong beliefs and misconceptions that had crept in.
God required that whenever He sent a new messenger, that messenger should be followed along with any new scripture given to him, superseding the previous changed/forgotten scripture teachings. This chain of messengers culminates in prophet Muhammad (peace on him), who is the last and final prophet and messenger. Since his prophethood, God's message is available unchanged and unadulterated, for the entire world, until the end of time. He wasn't sent as prophet and messenger for a specific group of people and specific time (e.g. as Moses and Jesus were to the Children of Israel), but he was sent for all the world, for all time, until the Day of Judgement. Thus he is the last, not first, prophet of Islam; a messenger to all mankind, for now, and for all time to come. He is the messenger who must now be followed.
And since the scripture given to him is the only one fully preserved. 100% the word of God, there won't be any need for a new Prophet, because the message is, and will remain, intact, as God has promised. Thus it is fully preserved with no word in it coming from any human, unlike the other scriptures that we have with us today, that have been changed by humans - thus it supersedes the previous scriptures, while being a continuation, confirmation and culmination of the original message contained within them, in its last and final form. The Final Testament. It has no versions or editions. Millions of people from all over the world have it memorised and they all recite word for word the same thing. It contains the central message of God, that people should obey God and His Messenger, and practical guidance on how to live, stories of previous prophets from which to learn lessons, warnings, rules, comfort, solace, good tidings, and in it God corrects misconceptions people may have about Him or His prophets. It tells us what has always been expected from humans since the beginning of time; what He told His prophets to teach people since the beginning. That message never changed. The essence of Islam is what always was, and has always been, the true and natural religion; the way of all the Prophets, the original and only message.
When you follow Islam, you are automatically following the central and core message God sent all the Prophets with, in its unchanged and original form. It is not a new faith, but is the same ultimate universal truth that God revealed to all the prophets, including Noah, Abraham, Moses and Jesus (peace be on them), and the same thing they all taught. Thus Islam is not named after a specific person (like Christianity, Buddhism), nor after a certain race or place (like Judaism, Hinduism), but a state of being, and is named by God Himself, the meaning loosely translating as 'submission to God', which is what every Prophet and their righteous followers did, from amongst all times, places and peoples. That in itself is one fraction of the evidence that it was the way of all the Prophets from the beginning.
As Muslims, we feel very close to Moses and Jesus (peace be on them both), and we love, honour, respect and believe in them. You would have no need to give them up, but if you did, you cannot be Muslim, as belief in them is a compulsory part of faith.
Peace.