beating 1.62% with index fund might not difficult?
The one year return on SPY is -12.4% right now. The chart is below. This has nothing to do with difficulty. Difficult implies you matter to the equation. Moving a desk might be difficult. Whether or not an investment beats an interest rate is about probability. Whether or not you'll need or want the this money or cash or something else is about probability, not difficulty.
I'm about as allergic to debt as it comes but 1.6% probably isn't enough to really be concerned about.
With that in mind, an 'index fund' is not 'safe'. Index funds are just the en vogue equity advice of the moment. Index investing is statistically the best way for the average person to maximize long term passive returns. Investing in a fund that tracks an index like the S&P500 is safER than buying a couple companies for reasons like you think Nike shoes are nice for essentially two reasons:
The average person doesn't have the funds to buy a sufficiently diversified portfolio regardless of the reasons for choosing the companies.
Non index tracking funds tend to be a lot more expensive. The bigger index funds like VOO or SPY have borderline negligible expense ratios, maybe 0.05% while an active managed fund might charge 0.75%. Extrapolate that cost over 10, 20, or 30 years and you've given up a lot of money to the manager.
Index funds are, however, not safe from losses. No matter what you do, you should always always always have a foundation of SAFE investments; something like a ladder of treasuries. Build a foundation of non-sexy safe investments.
I would not over prioritize repaying a 1.6% loan with interest rates rising as they are right now. In my opinion, right now, when 90 day treasuries are paying 2.3% (nearly double your interest rate) you would be better served by simply hoarding cash to ensure that you certainly don't take a car loan or other loan for any reason. Once you have a SAFE foundation, start clicking up the risk.
If your focus really is to 'earn as much as possible with reasonable risks,' just pay the loan faster. Because the rest of your question indicates that you don't really appreciate the risks.