How did our forefathers bake the dough they took out of Egypt? Would it qualify as matzo now?

Question

Shmos 12 (39) says:

“They baked the dough that they had taken out of Egypt as unleavened cakes, for it had not leavened, for they were driven out of Egypt, and they could not tarry, and also, they had not made provisions for themselves.”

Q1: How practically did our forefathers bake the dough? Did they improvise ovens and fuel or did they bake it on their backs in the sun as Targum Yonoson suggests?

Q2: Was the product of the baking halachic matzo as we understand it?

Since posing the questions I found at Yeshiva.co

Clearly one may not bake the matzot (for the the mitzva of eating matza) in the heat of the sun. If one did so, then even if the heat was very strong and it seems clear that the dough did not ferment, nevertheless one cannot use this matza to fulfill the mitzva of eating matza, for matza has been called "bread of poverty" in the Torah, and what is baked in the sun is not properly called bread (Shulchan Arukh Harav 461, 6).

Answer 1

Note that the Pasuk itself says "Ki Lo Chametz", but that phrase is up for interpretation. Mefarshim from here:

Or Hachaim takes the literal, halachic approach that @DoubleAA was referring to, and suggests that they were constantly kneading it, and that is why they had to place it on their backs:

מצות כי לא חמץ – פירוש הטעם שאפוהו מצות כי לא הותר להם לאכול חמץ לזה מהרו לאפותו מצה. והגם ששהה מעת לישה עד עת אפיה זמן מה. אולי כי היו מתעמלים בו, ולזה אמר הכתוב משארותם צרורות בשמלותם על שכמם, וכי לא היה להם מקום לשאת אותם שהוצרכו לתתם על שכמם, אלא כדי שיתעמלו בהם וכל זמן שמתעמלים בעיסה אינה מחמצת נוסף על שלא נתנו בו שאור לחמץ. ונתן הכתוב טעם כי לא חמץ כי גורשו ממצרים וגו׳.

Ibn Ezra suggests that it simply contained no leavening agent, and he, as well as one opinion in Ramban, and Chizkuni suggest that it was baked when they got to Sukkos.

To directly respond to your questions:

1) Ramban suggests (one opinion) that it was baked on the way, seemingly in ovens, whereas most other Mefarshim understand that it was baked in Sukkos. You already mentioned Targum Yonasan that the heat outdoors cooked it.

2) According to many Mefarshim, there was some reason or another why it did not rise, and might be considered Chametz in the Halachic sense. Seforno (based on Haggadah) says there was not enough time to rise. Shadal suggests that it was cooled down and didn't rise. Or Hachaim suggests that it was constantly being kneaded.

(See also the various other Mefarshim who offer additional interpretations of how it was maintained, and how it was baked.)