The restoration of all things started with the advent of Jesus,continuing to the building and rapture of […]
My understanding is that in Acts 3, Peter is having to address a people who did not expect the "My Servant Jesus" [SUFFERING] parts of a coming Messiah, but instead were anticipating (ONLY) a powerful and ruling one... and so Peter is pointing out that the OT scriptures ALSO spoke of the "suffering servant" aspects (which were thus fulfilled in their rejection of Him and His death on the cross).
Then Peter goes on to say that "whom heaven must receive UNTIL" (which speaks to the present time ["this present age [singular]"]--what some call the Church age [see the following scripture references]), and then speaks of "[until] the times of restoration [G605] of all things which God hath spoken of by the mouth of all His holy prophets since […]" (this is in contrast to what is later stated in Eph3:3-6,9; Col1:24-27; Eph1:20-23 "WHEN'; etc ["hidden in God"... "kept secret since" etc]), and which "G605" word ("restoration") has the following [per Bible Hub]:
[G605] "Cognate: 605 apokatástasis (from 600 /apokathístēmi, "restore") – restitution, referring to the "restoration of the physical earth in the Messianic kingdom (Millennium)" (G. Archer)."
...so I don't really see this starting (meaning the "whom heaven must receive UNTIL") not starting BEFORE His "the Lord Himself shall descend FROM HEAVEN with a shout" at the time of our Rapture (which I believe to take place BEFORE the opening of the FIRST SEAL/INITIAL "birth PANG [singular; 1Th5:2-3; Matt24:4/Mk13:5 "G5100 - tis - 'A CERTAIN ONE'"]" [which SEAL is] at the START of the 7-yr trib