Hey,
Its never too late in your career, yes, there is an age criteria factor which really matters for government exams. But as you told you have 3 years of experience and I guess you are in the age group to apply in government firms. If you are dedicated towards Government sector, you need to be prepared for many things, the work culture, environment, everything will be different. Getting into Govt firm is not easy this day, so prepare well if you really want to switch to that field.