This paper considers a Strongly Asynchronous and Slotted Massive Access Channel (SAS-MAC) where $K_n:=e^{nν}$ different users transmit a randomly selected message among $M_n:=e^{nR}$ ones within a strong asynchronous window of length $A_n:=e^{nα}$ blocks, where each block lasts $n$ channel uses. A global probability of error is enforced, ensuring that all the users' identities and messages are correctly identified and decoded. Achievability bounds are derived for the case that different users have similar channels, the case that users' channels can be chosen from a set which has polynomially many elements in the blocklength $n$, and the case with no restriction on the users' channels. A general converse bound on the capacity region and a converse bound on the maximum growth rate of the number of users are derived.