A lot of people are nervous about using used baby products, and for good reason. Safety standards change over time. What was considered safe three years ago might not be today. Some products, particularly those in the sleeping environment - such as cribs - can degrade and pose safety issues. In addition, products recalls happen and often go unnoticed. That's something particularly problematic when an item is passed along or sold at yard sale.
That having been said, you could use the seat - with a couple of caveats. Since you have been the owner all along you are fully aware of the condition of the seat and that's a big plus. Presumably, you'd have known if there was a recall, but not necessarily. So, that's the first caveat. You need to check to see whether there have been any reported safety issues with the seat. That's pretty easy to do. The National Highway Traffic Safety Administration maintains a database of car seat recalls and safety issues. For the most part, recalls are less involved that the word "recall" might imply. Usually, there is a resolution - sometimes a new part, sometimes new instructions - designed to resolve the safety issue. The second caveat applies more to others in a similar situation than to you. Car seats should never be used - regardless of condition - 10 years after they were made. And many car seats today actually come with expiration dates that are 5-8 years from the manufacture date.
So, as long as you're aware of, and address, safety issues and the seat is within the expiration range, you can feel comfortable using it for your new baby.