It is definitely feasible to start learning Oracle, especially if you have a solid IT background already. Some of the best DBAs I know have started their careers in another IT-related field, whether it be operating systems, programming or networking. A DBA must have knowledge in all of these areas, as well as in databases, so you already have a good start.
Being a DBA takes a special breed of individual -- some have what it takes, others do not. I would not suggest jumping right into spending a ton of money on Oracle training before you are sure it is the career path for you. I would suggest instead reading up on relational database concepts in general, then jumping into learning Oracle specifically. Since the best way to learn is often to do it hands on, download a free copy of Oracle for testing, do some Internet research, buy some good books, and start playing around with it. Again, being a DBA is not an easy career path and it will take a lot of hard work and learning to get there, but if you follow my advice, you will know soon enough if you have what it takes.
Good luck and let me know if you need further advice.
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