Even if you removed the article is Greek, it would only indicate that God is predicate, similar to Jn 1:1c.
NB: Removing the article to make "God" a predicate infers the activity or agency or power of God as in Jn 1:1c. Where the article is retained, i.e.
Jhn 4:24 ("[The] God is spirit") the person of God is being denoted,
However there are also cases, noted in Winer's Grammer (Omission of the Article before nouns - see below) where even anarthrous θεός will also denote the person of the Father (but not in Jn 1:1c - see further below).
(1) When the genitive θεου is dependent on another (anarthrous)
noun : L. iii. 2, Kom. iii. 5, viii. 9, xv. 7, 8, 32 \_Rec.~], 1 C. iii. 16,
xi. 7, 2 C, i. 12, viii. 5, E. v. 5, 1 Th. ii. 13.2
(2) In the phrases θεός πατήρ, 1 C. i. 3, 2 C. i. 2, G. i. 1, Ph. i. 2,
ii. 11, 1 P. i. 2 ; viol or τέκνα θεου, Mt v. 9, Rom. viii. 14,10, G-. iii.
26, Ph. ii. 15, 1 Jo. iii. 1, 2 (where these governing nouns also are
without the article 3).
(3) With prepositions : as άπο θεου, Jo. iii. 2, xvi. 30, Rom. xiii. 1
[Rec.], 1 C. i. 30, vi. 19 ; ἐv θεώ, Jo. iii. 21, Rom. ii. 17 ; ἐκ Θεοῦ, A.
v. 39, 2 C. v. 1, Ph. iii. 9 ; κατί θεόν, Rom. viii. 27 ; παρά θεω, 2 Th.
i. 6, 1 P. ii. 4. Similarly with an adjective in 1 Th. i. 9, θεω ζωντι
καϊ άλ-ηθινω.—I
n Jo. i. 1 (θεός ήν ο λόγος), the article could not have
been omitted if John had wished to designate the λόγος as ό θεός,
because in such a connexion θεός without the article would.be
ambiguous. It is clear, however, both from the distinct antithesis
πρός τόν θεόν, ver. 1, 2,. and from the whole description (Characterisirung)
of the λόγος, that John wrote θεός designedly. Similarly,
in 1 P. iv. 19 we find πιστός κτίστης without the article.