Did Alma the Younger expect everyone to have experiences like his?

Here is the first speech of Alma the Younger after his conversion.

And it came to pass after they had fasted and prayed for the space of two days and two nights, [that] the limbs of Alma received their strength, and he stood up and began to speak unto them, bidding them to be of good comfort:

For,

said he,

I have repented of my sins and have been redeemed of the Lord; behold I am born of the Spirit, and the Lord said unto me:

Marvel not that all mankind, yea, men and women, all nations, kindreds, tongues and people, must be born again; yea, born of God, changed from their carnal and fallen state, to a state of righteousness, being redeemed of God, becoming his sons and daughters; and thus they become new creatures; and unless they do this, they can in nowise inherit the kingdom of God.

I say unto you, unless this be the case, they must be cast off; and this I know, because I was like to be cast off. Nevertheless, after wading through much tribulation, repenting nigh unto death, the Lord in mercy hath seen fit to snatch me out of an everlasting burning, and I am born of God. My soul hath been redeemed from the gall of bitterness and bonds of iniquity. I was in the darkest abyss; but now I behold the marvelous light of God. My soul was racked with eternal torment; but I am snatched, and my soul is pained no more.

I rejected my Redeemer and denied that which had been spoken of by our fathers; but now, that they may foresee that he will come and that he remembereth every creature of his creating, he will make himself manifest unto all. Yea, every knee shall bow, and every tongue confess before him. Yea, even at the last day, when all men shall stand to be judged of him, then shall they confess that he is God; then shall they confess, who live without God in the world, that the judgment of an everlasting punishment is just upon them; and they shall quake, and tremble, and shrink beneath the glance of his all-searching eye (Mosiah 27:23-31).

If you read this quickly, it's easy to misread it as saying that the time when "he will make himself manifest unto  all" will be "at the last day, when all men shall stand to be judged of him." I don't think that's actually a possible reading of the text as we have it, though.

Alma says that "now, [in order] that they may foresee that he will come . . ., he will make himself manifest unto all." The purpose of this universal manifestation is to enable people to foresee that Christ will come, so it must occur before Christ comes and therefore not at the last day. I think the most natural reading is to take now literally, as referring to Alma's own time and his recent experience ("I rejected my Redeemer and denied that which had been spoken of by our fathers; but now . . ."). Alma seems to believe that now God is going to manifest himself to everyone, just as he did to Alma himself.

The connection with the statements about the "last day," I think is that the manifestation about to happen now will leave everyone without excuse at the last day. If he is going to "make himself manifest unto all," then none of those "who live without God in the world" do so out of ignorance; hence they confess that God's judgment is just.