"πορευθέντες οὖν μαθητεύσατε πάντα τὰ ἔθνη, βαπτίζοντες (baptize) αὐτοὺς εἰς τὸ ὄνομα (in the name) τοῦ πατρὸς (of the father) καὶ τοῦ υἱοῦ (of the son) καὶ τοῦ ἁγίου πνεύματος (of the holy spirit)..." (Matt. 28:19)
As we read, the apostles were instructed to invoke in the name (singular) of the following three (plural): the father, the son, and the holy spirit, each separate being serving a particular role, yet they all are the one God, and thus are called "God."
To better help you understand, consider there exists three separate states of water: solid, liquid, and gas, each serving a particular role, yet they all are water, and thus are called ''water."
How is the "state" of the Father different than the Holy Spirit? Isn't the Father also a spirit? If the Father is not Spirit and not flesh, then what is this third state?
If the Holy Spirit is a third person, it would be rude of Paul to ignore him:
1 Cor
Grace be unto you, and peace, from God our Father, and from the Lord Jesus Christ.
2 Cor
Grace be to you and peace from God our Father, and from the Lord Jesus Christ.
Romans
To all that be in Rome, beloved of God, called to be saints: Grace to you and peace from God our Father, and the Lord Jesus Christ.
Galatians
Grace be to you and peace from God the Father, and from our Lord Jesus Christ, Who gave himself for our sins, that he might deliver us from this present evil world, according to the will of God and our Father:
Ephesians
Grace be to you, and peace, from God our Father, and from the Lord Jesus Christ.
Colossians
To the saints and faithful brethren in Christ which are at Colosse: Grace be unto you, and peace, from God our Father and the Lord Jesus Christ.
Philippians
Grace be unto you, and peace, from God our Father, and from the Lord Jesus Christ.
1 Thess
Paul, and Silvanus, and Timotheus, unto the church of the Thessalonians which is in God the Father and in the Lord Jesus Christ: Grace be unto you, and peace, from God our Father, and the Lord Jesus Christ.
2 Thess
Paul, and Silvanus, and Timotheus, unto the church of the Thessalonians in God our Father and the Lord Jesus Christ: Grace unto you, and peace, from God our Father and the Lord Jesus Christ.
1 Timothy
Unto Timothy, my own son in the faith: Grace, mercy, and peace, from God our Father and Jesus Christ our Lord.
2 Timothy
To Timothy, my dearly beloved son: Grace, mercy, and peace, from God the Father and Christ Jesus our Lord.
Titus
To Titus, mine own son after the common faith: Grace, mercy, and peace, from God the Father and the Lord Jesus Christ our Saviour.
Philemon
Grace to you, and peace, from God our Father and the Lord Jesus Christ.
Hebrews
God, who at sundry times and in divers manners spake in time past unto the fathers by the prophets,
Hath in these last days spoken unto us by his Son, whom he hath appointed heir of all things, by whom also he made the worlds; Who being the brightness of his glory, and the express image of his person, and upholding all things by the word of his power, when he had by himself purged our sins, sat down on the right hand of the Majesty on high: Being made so much better than the angels, as he hath by inheritance obtained a more excellent name than they.
Other writers:
James
James, a servant of God and of the Lord Jesus Christ, to the twelve tribes which are scattered abroad, greeting.
1 Peter
Blessed be the God and Father of our Lord Jesus Christ, which according to his abundant mercy hath begotten us again unto a lively hope by the resurrection of Jesus Christ from the dead, To an inheritance incorruptible, and undefiled, and that fadeth not away, reserved in heaven for you, Who are kept by the power of God through faith unto salvation ready to be revealed in the last time.
2 Peter
Simon Peter, a servant and an apostle of Jesus Christ, to them that have obtained like precious faith with us through the righteousness of God and our Saviour Jesus Christ: Grace and peace be multiplied unto you through the knowledge of God, and of Jesus our Lord,
1 John
That which we have seen and heard declare we unto you, that ye also may have fellowship with us: and truly our fellowship is with the Father, and with his Son Jesus Christ.
2 John
Grace be with you, mercy, and peace, from God the Father, and from the Lord Jesus Christ, the Son of the Father, in truth and love.
Jude
Jude, the servant of Jesus Christ, and brother of James, to them that are sanctified by God the Father, and preserved in Jesus Christ, and called: Mercy unto you, and peace, and love, be multiplied.
No NT writer mentions him as a third person.
God is holy:
Psalm 99:9
Exalt the LORD our God, and worship at his holy hill; for the LORD our God is holy.
God is a Spirit:
John 4:24
God is a Spirit: and they that worship him must worship him in spirit and in truth.
The Father is the Holy Spirit. His manifestation in the flesh is Yeshua.