Learning to “play piano” actually describes a collection of many skills, and each must be built in careful balance and coordination with one another. Additionally, different people may have different definitions for having ‘learned piano’. But for most beginners, the idea of being able to play a favourite song without mistakes, and possibly from memory, would be a typical concept of what it would mean to have learned the piano.
The fastest way to achieve these benchmarks would be:
Work with a coach with whom you get inspired, and who can hold you accountable
Listen constantly to the music you are learning, both the exact song(s) as well as the style in general
Establish a daily practice routine that is highly structured and focus on the actual areas of work vs simply playing back your past achievements (a common error in people’s practice routines)
Ensure that you have a series of short, mid, and long term goals spread throughout the year so that your interest level stays high and there is a constant urgency to continue learning
Almost anyone, following the above and committing between 30-60 minutes daily to practice, could achieve a competent level of playing in as little as 18-24 months.