An Example from the first Christian Martyr
Most certainly the earliest Christians prayed to Jesus, as He Himself taught us to do (He explicitly "[does not mean He will] ask the Father for you," Jn 16:26 but that "[He Himself] will do it" 14:13-14; cf. 5:23).
The words on the lips of the deacon and first Christian martyr, Stephen, as he was being stoned to death were (Acts 7:59b W&H 1881):
Κύριε Ἰησοῦ, δέξαι τὸ πνεῦμά μου!
Lord Jesus, recieve my spirit!
In case you don't understand any Greek, 'Lord' appears in the vocative form here (Κύριε kyr·i·e), meaning He is speaking directly to Jesus, who at this point, of course, is in heaven (Acts 7:55).
An Example from the Most Prolific Apostle in the New Testament
St. Paul, the loyal servant of the Lord, besought the Lord Jesus that this affliction ("thorn in the side") from Satan would not plague him any more (2 Cor 12:8):
ὑπὲρ τούτου τρὶς τὸν κύριον παρεκάλεσα ἵνα ἀποστῇ ἀπ' ἐμοῦ
For this did I thrice beseech the Lord, that he might remove it from me,
However, the Lord elects to have St. Paul endure this suffering for His sake, and by His grace (12:9):
καὶ εἴρηκέν μοι Ἀρκεῖ σοι ἡ χάρις μου· ἡ γὰρ δύναμις ἐν ἀσθενείᾳ τελεῖται. Ἥδιστα οὖν μᾶλλον καυχήσομαι ἐν ταῖς ἀσθενείαις, ἵνα ἐπισκηνώσῃ ἐπ' ἐμὲ ἡ δύναμις τοῦ χριστοῦ
but he said to me, "My grace is sufficient for you: for power is perfected in weakness." Most gladly, therefore, will I rather boast in my weakness, so that the power of Christ might rest on me.
See also 1 Thessalonians 3:11; 2 Thessalonians 2:16-17; Colossians 3:17 etc.
St. John the Apostle Prays the Last Prayer Recorded in the New Testament
The last petition to anyone in the New Testament is to the Lord Jesus directly:
Λέγει ὁ μαρτυρῶν ταῦτα Ναί· ἔρχομαι ταχύ. Ἀμήν· ἔρχου, κύριε Ἰησοῦ
Thus says he that bears witness to these things: I am coming soon. (Amen! Come, Lord Jesus!)
Again, the vocative form of κύριος (Lord) is used, meaning John is speaking directly to Jesus, not expressing his desire that Jesus come to others reading: 'may the Lord Jesus come.'
There are of course other examples, but Jesus' own teaching suffices for this truth that we are to ask Him anything, and He will do it, not merely ask the Father for us. He explicitly rules out that interpretation of His answering prayer.