Michael Kruger at the Gospel Coalition says YES! Even though we don’t have the autographs (original manuscripts of Bible books), we still have very good reason to believe that the copies we have are reliable. He says that:
When it comes to the quantity of manuscripts, the New Testament is in a class all its own. Although the exact count is always changing, currently we possess more than 5,500 manuscripts of the New Testament in Greek alone. No other document of antiquity even comes close.
Kruger explains the difference between “autograph” and “original text.” His article introduces the topic of manuscript evidence clearly and concisely.
If you’re interested in understanding this important topic better, then check it out!