There is a famous Chasam Sofer (someone feel free to find the source inside and link) who notes that the whole point of Seder night is, as we are told in the Haggada:
בְּכָל־דּוֹר וָדוֹר חַיָּב אָדָם לִרְאוֹת אֶת־עַצְמוֹ כְּאִלּוּ הוּא יָצָא מִמִּצְרַיִם
In each and every generation, a person is obligated to see himself as if he left Egypt.
This experience is likened to that of a ger (a convert) who does not make a bracha upon his tevillah (immersion) in a mikvah (ritual bath) until after he comes out. The reason being, because prior to entering the water he was still a non-Jew and could not say:
בָּרוּךְ ... אֲשֶׁר קִדְּשָׁנוּ בְּמִצְוֹתָיו וְצִוָּנוּ עַל הַטְּבִילָה
Who has commanded us concerning immersion (refer to Tosafos s.v. al hatevillah - Pesachim 7b)
Therefore, so too with the case of seder night, it is only after we complete re-telling the story of the Jewish peoples' liberation from slavery, that we feel like we were personally there and can only make a bracha after this point but not before.