you can become member of an A-kasse, also if you are unemployed.
But normally it gives no meaning to become member as unemployed, because - as you say your self - you must be able to meet the income-requirement. The income-requirement says that you must have earned/have had an income of at least DKK 233,376 (in 2019) during the last 3 years (in total). Only income earned during membership-periods can be included.
The most jobs will give you sufficient salary/income to meet the income-requirement in 1 year. And for being eligible for dagpenge there is also a requirement of minimum 1 year membership (up to the date you apply for dagpenge).
So normally people become member when they get a job, and then they will be eligible for dagpenge after 1 year.
Anders Weber, www.a-kasser.dk