Is it wise to day trade without being subscribed to real-time data?

Trading delayed data in a paper trading account has value for learning to function efficiently on that broker's platform but not much more than that.

IBKR's delayed quotes are 10-20 minutes behind real time data. It's possible to trade with delayed data but whether your order will be filled or not will be determined by current prices. Effectively, you're trading while blind.

Try to find a secondary source of real time data. Otherwise, forget this idea.

By "real-time" data I assume you don't mean nanosecond freshness but just "not delayed by many minutes". If so, this is a standard service all brokers provide. They even have some basic data for free on their sites without an account, and many brokers these days let you open accounts with no minimum and no fees. I would start there. The data you see will be up to a few seconds or milliseconds behind the actual trades being placed, depending on the quality of the broker.

If you do want nanosecond-fresh data, then your question makes no sense. Network latency and processing power becomes critical at that point (this is where people rent buildings across the street from NYSE and turn them into datacenters) and it takes millions of dollars, which you don't have.

Trading with even a 15 minute delay, in principle, is doable. Many trends develop over hours or days. If you can design a strategy to target those and be neutral against the second and minute level trends, you could do it. But keep in mind for example that if you see a stock shooting up, so you buy it, and your data is 15 min delayed while the stock crashed 10 minutes ago, you'll lose a bit of money. If you bid $100 for a stock that's now $20 the broker won't charge you $100 and pocket the $80 btw, they will just buy it at the best price. But I've also never heard of a broker that lets you place live orders but doesn't give you live quotes - sounds like it would probably be illegal to do that.

Anyways, if you want to get a taste for day trading but don't even have a couple hundred, the best thing to do is paper, aka fantasy trading. If you go by only your delayed data and never cheat by peaking at real world news and so on, it will be exactly the same (except that the money isn't real). You could also open a robinhood account and trade 0.0001 shares, but if you're actively trading you'll get a fat tax form at the end of the year and CPAs charge a couple hundred anyhow.

Also, in the US I believe there's a law that requires a >$30k balance to day trade, which they define as "selling the stock the same day it was bought more than 3 times in a week". So once again, day trading without funds is not practical.