16 weeks okay to start foods?

My daughter is 16weeks on Sunday but won’t be 4months technically until the 20th. She was born 8/20. She has been very advanced in head control and has been sitting on her own for a few weeks. She has not been gaining a whole bunch of weight and seems constantly hungry. She’s 13.5lbs. Have any moms started cereals or purées at this time? She is extremely interested in my food. She won’t see her doctor until December 29th when she will be almost 19weeks. I just want to see if anyone has advice.