If Jesus is "God's Only Son" then how can we all be God's children? In the Apostle's creed it states that "I believe in Jesus Christ God's only son our Lord" (ELCA). But many Christians say that we're all God's children, which is contradictory.

What does the Bible have to say about this?

Or are we God's grandchildren and Jesus' children?
The Latin text of the Apostle’s Creed (Symbolum Apostolicum) states,

Credo in Deum Patrem omnipoténtem, Creatórem cæli et terræ, et in Iesum Christum, Fílium Eius unicum, Dóminum nostrum, qui concéptus est de Spíritu Sancto, natus ex Maria Virgine, passus sub Póntio Piláto, crucifixus, mórtuus, et sepúltus, descéndit ad ínferos, tértia die resurréxit a mórtuis, ascéndit ad cælos, sedet ad déxteram Dei Patris omnipoténtis, inde ventúrus est iudicáre vivos et mórtuos.

While the Latin word unicum (lemma unicus) can certainly be translated into English by the word “only,”1 St. Jerome also used it in the Latin Vulgate to translate the Greek word μονογενὴς,2 meaning “only-begotten.”
For example, in Luke 7:12, it is written,

ΙΒʹ ὡς δὲ ἤγγισεν τῇ πύλῃ τῆς πόλεως καὶ ἰδού, ἐξεκομίζετο τεθνηκὼς υἱὸς μονογενὴς τῇ μητρὶ αὐτοῦ καὶ αὐτὴ ἦν χήρα καὶ ὄχλος τῆς πόλεως ἱκανὸς σὺν αὐτῇ TR, 1550
XII cum autem adpropinquaret portae civitatis et ecce defunctus efferebatur filius unicus matri suae et haec vidua erat et turba civitatis multa cum illa Vul

Other times, he translated μονογενὴς by the Latin word unigenitus,3 which is the Latin equivalent of “only-begotten.”4
Therefore, we could properly translate the Latin word unicum in the Apostles’ Creed as “only-begotten” (rather than “only”) without causing a contradiction, since Christians are also children (sons and daughters) of God,5 just as angels are sons of God.6
The important point to emphasize is the Lord Jesus Christ is the only-begotten (or, only-born) son of God the Father, by an eternal generation. The Lord Jesus Christ said, “I came out of God and have arrived.”7 This is the only instance where the Lord Jesus Christ says ἐξῆλθον ἐκ τοῦ θεοῦ. In the LXX, this phrase, the lemma ἐξέρχομαι + the preposition ἐκ, is used in reference to the generation of offspring.8
On the other hand, Christians are sons of God by regeneration, i.e. being born again.9

References
Lewis, Charlton T.; Short, Charles. A New Latin Dictionary. New York: Harper, 1891.
Footnotes
1 Lewis &amp; Short, unicus, p. 1932
2 Luke 7:12: unicus; Luke 8:42: unica; Luke 9:38: unicus
3 Jdg. 11:34: unigenita; John 1:14: unigeniti; John 1:18: unigenitus; John 3:16: unigenitum; John 3:18: unigeniti; Heb. 11:17: unigenitum; 1 John 4:9: unigenitum
4 Lewis &amp; Short, unigenitus, p. 1932
5 cp. John 1:12: τέκνα θεοῦ
6 cp. Job 1:6. The LXX translates the Hebrew בְּנֵי הָאֱלֹהִים into Greek as οἱ ἄγγελοι τοῦ θεοῦ.
7 John 8:42
8 cp. Gen. 15:4, 35:11