First and foremost the doctrine of the trinity is not an "assumption." It is the normative systematic theology of God in Christianity and is BASED on the fact that the Bible is explicit in telling us that there is, was and forever will be only ONE God AND the fact that the Bible identifies three (and only three) persons as God.
So, explaining the nature of the one God is the whole point of the doctrine of the trinity. That is its goal and it does so by IDENTIFYING God in MANY different contexts that reveal His UNIQUE attributes usually manifested by His UNIQUE actions.
The Bible identifies God by, 1.) His names. 2.) His titles. 3.) His unique attributes. 4.) His unique actions. 5.) His worship. I am not aware of any other literary, contextual means by which the Bible clearly identifies God. I could be wrong, but I think this list is comprehensive.
If you will examine the Bible thoroughly you should be able to quickly discover that there are three and ONLY three "persons" who are identified as God by the COMBINATION of the literary means listed above.
These persons are each variously... 1.) CALLED by the NAMES of God, (YHWH, and its variants) either directly or indirectly, usually both.
2.) RECOGNIZED with the TITLES of God, (Lord, king, savior, redeemer, etc.
3.) ATTRIBUTED with the UNIQUE characteristics of God, (omnipresence, omnipotence, omniscience, eternality,)
4.) CREDITED with the UNIQUE actions of God, (creation, origin of God's word, salvation of men and/or creation, etc.
5.) WORSHIPED and/or given the honor, reverence and position due to God ALONE etc.
I am NOT saying that the Father, Son and Holy Spirit are all consistently, equally and in every mention identified as God in every place they are represented in the Bible by any combination of these 5. Nor am I saying that each person of the trinity is represented equally by ALL FIVE of these means of identifying God.
I AM saying, 1.) that each person of the trinity receives some COMBINATION of these 5 means of identifying and distinguishing God listed above. 2.) ONLY the three persons of the trinity receive some COMBINATION OF THESE 5.
The Bible does not attribute creation (a UNIQUE act of God alone) to any person other than those to whom it ALSO refers to as "God" by name or title and to whom is also attributes other unique actions or attributes that identify "God."
Looking at it from another point, the Bible does not call anyone "God" (in the proper sense - meaning THE one and only God) to whom it does not attribute the UNIQUE actions and UNIQUE attributes of God.
Looking at this from the negative, the Bible does NOT attribute the UNIQUE CHARACTERISTICS of God, such as omnipresence or eternality, to anyone whom it does NOT call "God" (by name and/or title) in the proper sense.
The Bible never attributes omnipresence or eternality to anyone whom it does not call "God" and /or shows being worshiped. Again, there are only three persons in the whole Bible who meet this criteria for identifying God.
To make solid my point you have for example at Isaiah 40:4, "I, the Lord, am the first, and with the last. I am He." Revelation 1:17-18 where Jesus is speaking, "Do not be afraid; I am the first and the last, and the living One; and I was dead, and behold I am alive forever more, and I have the keys of death and Hades."
Another example from Isaiah 43:11. "I, even I, am the Lord; And there is no savior besides Me." Luke 2:11, "for today in the city of David there has been born for you a Savior, who is Christ the Lord."
The last example from Isaiah 44:24, "Thus says the Lord your Redeemer, and the one who formed you from the womb, "I, the Lord, am the maker of all things, Stretching out the heavens BY MYSELF, And spreading out the earth ALL ALONE."
John 1:3, "All things came into being by Him, and apart from Him nothing came into being that has come into being." Colossians 1:16, "For by Him all things were created, both in the heavens and on earth, visible and invisible, whether thrones or dominions or rulers or authorities--all things have been created by Him and for Him."
The list of examples could go on but I think you get the point. A true understanding (within human limits) of who God IS, is essential to a valid relationship with Himself according to His own purpose. No valid, systematic theology can be drawn by reducing or eliminating scriptural evidence. We must account for ALL of God's revelation to come to a realization of who God is and what He has done and therefore what His very nature is.
God has revealed Himself to us in different ways at different times as the Biblical revelation unfolded over time according to His eternal purpose. It is ONLY accounting for ALL of this revelation that we can know Him as He has revealed Himself.
BUT theology is NOT salvation. It is in Christ that we find God fully and sufficiently manifested to us human beings, AS a human being and for His own glory. And it is only through His Holy Spirit that we can know Him and be saved by His grace.
I'm sure you have heard the question, "Is the Trinity a requirement for salvation?" Personally, I say no. I do not believe trinitarianism is a REQUIREMENT for salvation. It is the RESULT of salvation. One cannot know Jesus Christ and somehow miss the fact that he is God. You cannot have experienced the presence of the Holy Spirit of God and somehow miss that He is God.
Romans 8:9-11, "But if the Spirit of Him who raised Jesus from the dead dwells in you, He who raised Christ Jesus from the dead will also give life to your mortal bodies through His Spirit who indwells you."