My sense is that the Hebrew here is poetic and ambiguous. However, I think the verse should not be understood as referring to the time period in Egypt before the Exodus. Instead, the verse references God taking his people out of Egypt and the forty years spent in the desert/wilderness prior to their entrance into the land of Israel.
Hosea 13:4-5 is similar to 11:1 and ambiguous in exactly the same way, but the focus on the post Exodus experience is clear:
But I have been the Lord your God
ever since you came out of Egypt. You shall acknowledge no God but me,
no Savior except me. I cared for you in the wilderness,
in the land of burning heat. (Hosea 13:4-5 NIV)
Hosea is talking to a people who are on the verge of exile. Religiously, the Israelites have become obsessed with ritual and have neglected social justice.
I fell in love with Israel when he was still a child" (Hosea 11:1).
This prophecy, like many others around this time, romanticizes the time period before the establishment of a monarchy in Israel. For the prophets, the time spent wandering in the desert following the Exodus was one of complete dependence on God and is related to the metaphor of God being the shepherd of his people (Jeremiah 23:1-4 and Ezekiel 34:1-31).
The desolation of the desert symbolizes an emphasis on a pure relationship between God and individuals and a de-emphasis on religious ritual:
‘I remember the devotion of your youth,
how as a bride you loved me and followed me through the wilderness,
through a land not sown. Israel was holy to the Lord,
the firstfruits of his harvest... (Jeremiah 2:2-3)
This is what the Lord Almighty, the God of Israel, says: Go ahead, add
your burnt offerings to your other sacrifices and eat the meat
yourselves! For when I brought your ancestors out of Egypt and spoke
to them, I did not just give them commands about burnt offerings and
sacrifices, but I gave them this command: Obey me, and I will be your
God and you will be my people. Walk in obedience to all I command you,
that it may go well with you (Jeremiah 21:21-23).
In summary, the Later Prophets are replete with references to the Exodus from Egypt and the subsequent covenantal relationship that was forged in the desert/wilderness prior to entrance into the land of Israel (Isaiah 11:16 is another clear example). Therefore, Hosea 11:1 should be understood as referring to the time period after the Exodus from Egypt.
The image of God shepherding his people in the desert after the Exodus is particularly poignant because the eventual exile from Israel is described by the prophets as a return to the desert context and that type of a relationship with God. For example, Hosea 12:10:
I have been the Lord your God
ever since you came out of Egypt; I will make you live in tents again,
as in the days of your appointed festivals.
Also, Hosea 3:4:
For the Israelites will live many days without king or prince, without
sacrifice or sacred stones, without ephod or household gods.
Also relevant to this theme is Jeremiah's plea in Jeremiah 9:1.