The Bible does indeed use the analogy of sleep to describe the state of the dead (1 Thessalonians 4:13 1 Thessalonians 4:13But I would not have you to be ignorant, brothers, concerning them which are asleep, that you sorrow not, even as others which have no hope.
American King James Version×; 1 Corinthians 15:51 1 Corinthians 15:51Behold, I show you a mystery; We shall not all sleep, but we shall all be changed,
American King James Version×, etc.). Those who have died are totally unaware of the passage of time and feel no pain or sorrow (Ecclesiastes 9:5 Ecclesiastes 9:5For the living know that they shall die: but the dead know not any thing, neither have they any more a reward; for the memory of them is forgotten.
American King James Version×, 10). They will be "awakened" at the time of the resurrection. But this does not require that their physical bodies persist until that time.
Scripture reveals what happens to our physical bodies after death. Genesis 3:19 Genesis 3:19In the sweat of your face shall you eat bread, till you return to the ground; for out of it were you taken: for dust you are, and to dust shall you return.
American King James Version×tells us that we will return to dust. If moisture and air are present, even our bones will eventually disintegrate. In the final analysis, there is no difference between the dust of decomposition and the ashes of cremation.
Neither will have any effect whatever on God's sure promise to resurrect all human beings in due course according to His plan and purpose (1 Corinthians 15:22 1 Corinthians 15:22For as in Adam all die, even so in Christ shall all be made alive.
American King James Version×; John 5:28-29 John 5:28-29  Marvel not at this: for the hour is coming, in the which all that are in the graves shall hear his voice,  And shall come forth; they that have done good, to the resurrection of life; and they that have done evil, to the resurrection of damnation.
American King James Version×; Revelation 20:4-6 Revelation 20:4-6  And I saw thrones, and they sat on them, and judgment was given to them: and I saw the souls of them that were beheaded for the witness of Jesus, and for the word of God, and which had not worshipped the beast, neither his image, neither had received his mark on their foreheads, or in their hands; and they lived and reigned with Christ a thousand years.  But the rest of the dead lived not again until the thousand years were finished. This is the first resurrection.  Blessed and holy is he that has part in the first resurrection: on such the second death has no power, but they shall be priests of God and of Christ, and shall reign with him a thousand years.
American King James Version×; Revelation 20:11-14 Revelation 20:11-14  And I saw a great white throne, and him that sat on it, from whose face the earth and the heaven fled away; and there was found no place for them.  And I saw the dead, small and great, stand before God; and the books were opened: and another book was opened, which is the book of life: and the dead were judged out of those things which were written in the books, according to their works.  And the sea gave up the dead which were in it; and death and hell delivered up the dead which were in them: and they were judged every man according to their works.  And death and hell were cast into the lake of fire. This is the second death.
American King James Version×)—which must include those who have been cremated.
Faithful Christians will be resurrected with spirit bodies (compare 1 Corinthians 15:35 1 Corinthians 15:35But some man will say, How are the dead raised up? and with what body do they come?
American King James Version×; 1 Corinthians 15:45 1 Corinthians 15:45And so it is written, The first man Adam was made a living soul; the last Adam was made a quickening spirit.
American King James Version×; 1 Corinthians 15:49 1 Corinthians 15:49And as we have borne the image of the earthy, we shall also bear the image of the heavenly.
American King James Version×). The rest of mankind who died in past ages, beginning with the nation of Israel, will be reconstituted in the flesh (see Ezekiel 37) before being offered immortality.
On the overall questions of death and the future, you'll find more details spelled out in our free booklets What Happens After Death? and Heaven and Hell: What Does the Bible Really Teach?