Is the Bible we have today the same Bible that was circulating in the first century? Yes.
We have every reason to believe that our English Bibles are tremendously accurate, and agree with the originally-inspired Greek and Hebrew languages in which God’s Word was first recorded by the inspired human authors. For those who suggest that various levels of corruption or human invention have been introduced to the text over the centuries, there is a discipline called “textual criticism” that helps protect the integrity of the biblical text. To be super (too?) brief (and maybe a little confusing if you’re new to this), textual criticism weighs internal and external manuscript evidence to help us accurately identify which words the Gospel writers, the Apostle Paul, or any other biblical author actually wrote. And within the last few weeks, an evangelical expert in textual criticism by the name of Daniel Wallace has hinted at recent findings that will further strengthen an already-compelling case for the validity of the New Testament.