The "will of God" could be inferred in the verse from the ellipsis. The verse can be translated like the ISV and TLB to take the discourse aspect of the literature into consideration:
ISV who were born, not merely in a genetic sense, nor from lust, nor from man’s desire, but from the will of God.
TLB All those who believe this are reborn!—not a physical rebirth resulting from human passion or plan—but from the will of God.
I agree that the will of is not necessarily inferred for God, however wouldn't object to it.
Ellipsis is common in ancient Greek. David Mathewson writes in Intermediate Greek Grammar 2016, in chapter Discourse Considerations:
13.2. Most discourses, at some level, are meant to be coherent. We assume that the NT authors were trying to make sense and communicate something to readers and that the various units that make up their discourses are meant to be related in some way (in other words, discourses are understandable, as opposed to being a string of unrelated, jumbled statements that make no sense).6 Cohesion refers to the linguistic elements that an author uses to weave a discourse together. Cohesion links something in the text to something that has come before it. These linguistic elements provide signals for readers, showing how the discourse has been constructed and how readers should put it together. According to Young, “cohesion is the glue that holds a discourse together” (254). Various means are used in the NT to provide cohesion.
13.11. Ellipsis. A further important cohesive device is ellipsis. This occurs when the repetition of a word, group of words, or clause can be left out because it is understood to be carried over from a previous clause. To give another English example, if a person answers “Five” to the question “How many deer did you see?” the answer has elided, or left unexpressed, the words “I saw _________ deer.” These words are assumed from the question “How many deer did you see?”
οὐ μόνον δέ, ἀλλὰ καὶ καυχώμεθα ἐν ταῖς θλίψεσιν, εἰδότες ὅτι ἡ θλῖψις ὑπομονὴν κατεργάζεται, ἡ δὲ ὑπομονὴ δοκιμήν, ἡ δὲ δοκιμὴ ἐλπίδα. (Rom. 5:3–4) And not only [do we boast in the hope in God’s glory], but we also boast in tribulations, knowing that tribulation produces endurance, and endurance [produces] proven character, and proven character [produces] hope.
Ellipsis is grammatically necessary, but logically unnecessary. It is most common in adverbial clauses like while [I was] taking notes.
John 4:1-2 Therefore when Jesus knew that the Pharisees had heard, "Jesus is making and baptizing more disciples than John
was making" (although Jesus himself did not baptize, but his disciples
See, Gerald Steven's New Testament Intermediate Greek. In the same way, the phrase will of is definitely implied, the author need not repeat will of in every list or sentence of the argument. The argument is about the source of begetting of the children of God, it shows the meaning of being spiritual. It has nothing to do with the determinism or fatalism as in Manichaeanism, of course.
1 Cor 3:9 says, "For we are God's fellow workers. You are God's field, God's building". Dan Wallace (Exegetical Syntax, 130) sees an ellipsis here, he misinterprets it as, "we are fellow-workers (with each other) for God; however, it's a deliberate interpretation, changing it to possessive genitive; it ignores the context v6-7 that they worked, however, God made them grow, thus, working together with God, as his servants. Paul says, we, the apostles as the co-workers with God working on you the field and building of God. The referent you are is only used with God's building, it is obvious that the same [you are] applies to God's field too. The phrases "my fellow worker" is a different phrase, thus, Mayer refutes,
Θεοῦ συνεργοί] for we, your teachers, labour with God, the supreme Lord and Fosterer of the church, at one work, which is simply the furtherance of the church. The explanation: workers who work with each other for God’s cause (Estius by way of suggestion, Bengel, Flatt, Heydenreich, Olshausen), is linguistically erroneous (see 1Th 3:2; Rom 16:3; Rom 16:9; Rom 16:21; Php 2:25; Php 4:3; 2Co 1:24; 2Ma 14:5; Plato, Def. p. 414 A; Dem. 68. 27, 884. 2; Plut. Per. 31; Bernhardy, p. 171; Kühner, II. p. 172), and fails to appreciate that lofty conception of a δοῦλος Θεοῦ.