It would be instructive to re-ask this question as "what would you do to pay for a $400 dollar expense in 6 months". I suspect the answer would be different. There's very good evidence to show that people are bad at planning for nebulous future risks, especially compared with current needs/wants.

Robinhood should add a direct-deposit option which automatically buys shares of indexes in a preset mix once sufficient capital has been deposited, I suspect that would materially help.

In Australia this actually happens in a rather structured way; Superannuation, or defined contribution benefits as it is usually called in Europe. Your employer (full or part time) is required by law to contribute 9.5% of your salary (over the top) into a regulated fund with your name on it (i.e. the funds are no longer accessible to the company). In your younger years this is normally put into a growth focused investment (stocks etc), when you get closer to retirement most employees elect to move to a more cash / hard asset class (bonds, property, and sometimes corp bonds). The real pity is that most super administration companies charge whopping fees and most employees stick with the administrator chosen by their company.

Alas, the superannuation is mostly restricted to fairly expensive options, ie high fees. That's because providers have to clear some regulatory hurdles keeping competition down. You can't just tell the government "Yeah, I'm using vanguard index funds for my mandatory 9.5%."

At the moment, Host Plus might be the best option (read 'cheapest option') for Australians. Not sure if that's still the case.

You can set up a self managed super fund (SMSF)[0], you do become the trustee of your own super fund and you do need to follow super regulations but it does give you the ability to a large percentage if not all your super money into a low fee index fund.

[0] https://www.ato.gov.au/Super/Self-managed-super-funds/Thinki...