Some believe Jonah really sank and got swallowed/spit up. Others suppose the story of Jonah was always meant to be understood as a parable. I'll suspend judgment today because either view would support the one point I'm about to make here.
In the fish, Jonah prays: "I called out to the Lord, out of my distress, and he answered me; out of the belly of Sheol I cried, and you heard my voice. ... I remembered the Lord, and my prayer came to you, into your holy temple." (2:2,7)
Now, whether this prayer was fictionalized historically in situ - or whether it was actually retold by a miraculous survivor - doesn't matter at all, at the moment. Either way, this is one of those details that dates the story of Jonah to within a century or so after Solomon's Temple was built.
Thus we have Jonah, in the belly of the fish, describing how his prayer must have been heard by God's super hearing, and carried all the way to Jerusalem. Because that's where God lives. And hears prayers from. According to Jonah.
But compare that with these famous verses of David's: "If I ascend to heaven, you are there! If I make my bed in Sheol, you are there! If I take the wings of the morning and dwell in the uttermost parts of the sea, even there your hand shall lead me, and your right hand shall hold me." (Psalm 139:7-10)
The Psalmist believed God could go anywhere. Did the figure of Jonah really believe God was only in Solomon's Temple? David's God took him by the hand, held and led him directly. Jonah's God worked indirectly, from afar, using indirect means that (although super-incredible) were completely natural. Weather cast Jonah down. Seaweed grabbed hold of him. A fish brought him up.
In sum, I'd argue that the close, grasping hand of God from Psalm 139 is not even hardly conceived of by Jonah's prayer. So to those who wonder if Jonah really believed he could get away from the Lord, I suggest - yeah. He did. Just like it says: "Jonah rose to flee to Tarshish from the presence of the Lord." (1:3)
And now, here is my point.
Fact or fiction, Jonah's story reflects a time after Solomon got God to live in a Box. David's Psalm reflects a more primitive faith in the nomadic God of the Ark and the Tabernacle.
Do with that as you may...