Here is timeline with references:-
1947:- independence and the first constituent assembly meets (CAP). Tasked with drafting constitution, etc.
Jan 1948:- CAP appoints Usmani elected shaykh Al Islam, head mufti. He will be the main interlocutor on the drafting committee with the ulema and the real author of the objectives resolution.
https://etheses.whiterose.ac.uk/4235/2/DX087128_2.pdf
Early 1948:- Zafarullah Khan is appointed to head the committee- this caused tension with the more conservative ulema, him being Ahmadi and all.
http://pu.edu.pk/images/journal/history/PDF-FILES/17_56_1_19.pdf
Mid 1948:- The JUP draft principles that must be accepted in the constitution. Jinnah accepted the draft of proposal about the Islamic nature of the state that the JUP had drafted and said it would be incorporated into the constitution.
Ahmad, Jam‘iyyat ‘Ulama-i-Pakistan 1948-79, 5.
Date Inferred- Mid 1948:- Zafarullah headed committee to draft the resolution and that it had input from ulema.
https://www.dawn.com/news/1530114
September 1948:- Jinnah dies.
https://en.m.wikipedia.org/wiki/Muhammad_Ali_Jinnah
March 1949:- Liaquat Ali presents the objectives resolution.
https://en.m.wikipedia.org/wiki/Objectives_Resolution#:~:text=The resolution proclaimed that the,under Article 2(A).
March 1949:- Zafarullah defends the objectives resolution when it is presented
https://tribune.com.pk/story/1306912/road-not-taken?amp=1
Btw, what is available in public on the internet is heavily biased side of history. And it is confused. They can’t agree who actually drafted the resolution whether it was Liaquat Ali, Usmani or Zafarullah.
The salient thing is that Jinnah chose an Ahmadi to lead the committee and he also had the ulema advise on it. This was intentional on his part because he wanted to get an Islamic republic that protected minorities.