Individuals under age 65 are eligible to contribute to a Health Savings Account (HSA) if they are enrolled in a Qualified High-Deductible Health Plan. The Qualified High-Deductible Health Plan must be be in place before an HSA account can be opened.
Persons age 65 and over can maintain an HSA established prior to age 65, but they can no longer make contributions into the HSA.
An HSA cannot be established for persons eligible to be claimed as a dependent on another person's tax return. This means HSAs are essentially limited to adults. You cannot establish a stand-alone HSA for a tax-deductible dependent child.
Unless coverage is being provided through an employer-sponsored plan, your HSA-compatible health insurance will be subject to normal insurance company underwriting requirements.
If ongoing medical circumstances have prevented you from obtaining traditional medical insurance, you are unlikely to get a better outcome in applying for an HSA-compatible health plan.