The phrase ὁ λόγος τοῦ Θεοῦ (= the word of God) occurs in (slight) variations in 42 places such as Matt 15:6, Mark 7:13, Luke 5:1, 8:11, 21, 11:28, John 10:35, acts 4:31, 6:2, 7, 8:14, 11:1, 12:24, 13:5, 7, 46, 17:13, 18:11, Rom 9:6, 1 Cor 14:36, 2 Cor 2:17, Col 1:25, 1 Thess 2:13, 1 Tim 4:5, 2 Tim 2:9, Titus 2:5, Heb 4:12, 5:12, 13:7, 1 Peter 1:23, 2 Peter 3:5, 1 John 2:14, Rev 1:2, 9, 6:9, 17:17, 19:9, 13, 20:4.
A number of these discuss "hearing" the word of God (Luke 5:1, 8:21, 11:28, Acts 13:44, etc). In Rev 1:2, John uses the term "ὁ λόγος τοῦ Θεοῦ" in a technical sense that can be deduced from the well-known "chain of Revelation"; here John appears to use the phrase to mean the testimony about Jesus which is "heard" (v3).
BDAG lists many of the above texts and simply observes:
The apostles and other preachers with reference to the λόγος τοῦ Θεοῦ
are said to λαλεῖν Acts 4:29, 31, 13:46, Phil 1:14, Heb 13:7;
κατήγγελλον Acts 13:5, 17:13; διδάσκων Acts 18:11; μαρτυρίαν Rev 1:2.
Of their hearers it is said: τὸν λόγον τοῦ Θεοῦ ἀκοῦσαι Acts 13:7;
δέδεκται Acts 8:14, 11:1. Of the λόγος τοῦ Θεοῦ itself we read
ηὔξανεν Acts 6:7, 12:24, 19:20; οὐ δέδεται 2 Tim 2:9. In these places
and many others ὁ λόγος τοῦ Θεοῦ is simply the Christian message, the
Gospel: Luke 5:1, 8:11, 21, 11:28. … Since the 'divine word' is
brought to humanity through Christ, his word can be used in the same
sense: τὸν λόγον μου John 5:24 …
Now specifically to 1 Thess 2:13. The word "λόγος" occurs three times as follows:
- hearing the word of God from us
- you accepted not the word of men/humans
- but it is truly the word of God
The fact that what the apostles preached as the word of God and it was heard by the listeners, not as the word of humans but truly the word of God, suggests that "word of God" here is the spoken word, more specifically the Gospel message. I also observe that the word of God has a work to do on the hearers - presumably transforming them (via the work of the Holy Spirit) into Christians worthy of the title.
Therefore, "λόγος" in 1 Thess 2:13 means the (spoken) Gospel message of the apostles.