We can check
Nobody has the original pages written by Moses, Isaiah or John. Every ancient book reached us the same way, copied by hand, again and again.
So the real question is whether the copies can be checked. For the Bible, they can, better than for any other book from the ancient world.
The New Testament
More than 5,800 handwritten Greek copies of the New Testament have been catalogued, and over 20,000 more in other languages. They were copied in different centuries, in different countries, by people who never met.
If anyone had changed a passage, the change would show up against all the copies that don't have it. With thousands of witnesses, nobody can slip a change past the rest.
The oldest scrap, a page of John 18 now in Manchester, was copied in the second century.
The Old Testament
Until 1947, the oldest Hebrew copies of the Old Testament dated from around the tenth century AD. Then shepherds found the Dead Sea Scrolls.
The scrolls include a complete copy of Isaiah made around 125 BC, a thousand years older than any copy we had. Set side by side, they are the same book.
Older still
In 1979, archaeologists in Jerusalem found two tiny silver scrolls, worn as amulets before Babylon destroyed the city in 586 BC. Scratched into the silver is the blessing God gave Moses:
"The Lord bless thee, and keep thee. The Lord shew his face to thee, and have mercy on thee. The Lord turn his countenance to thee, and give thee peace."
Numbers 6:24 to 26
Twenty-six centuries later, that is still the blessing in your Bible.
The straight answer
We know the Bible hasn't been changed because the oldest copies have been found, and they say what our Bibles say. Thousands of New Testament copies agree with one another. Old Testament scrolls copied before Jesus was born match the copies made a thousand years later.
Isaiah said it long before anyone could check: "the word of our Lord endureth for ever" (Isaias 40:8). And Jesus: "Heaven and earth shall pass away, but my words shall not pass away" (Matthew 24:35).