I lived in 3rd floor walk-up in NYC when I got Maggie at 8 weeks old. She walked up the stairs from day one with no problems. It took about a month for her to get the courage to try and go downstairs on her own.
I asked the same question when I got Maggie and was informed that it would not harm them. I see no ill effects to Maggie from her having walked up and down the stairs for her first year of life. I just made sure to let her take it at her own speed and if she was too tired, I always carried her.
Good luck.