The difference between being busy and ignoring someone is actually noticeable, but there's a catch you should understand: in the early stages, right after a first date, how fast you respond can say something about your level of interest. Not because it's a rule, but because people who want to develop a relationship usually make time for messaging. If he's responding quickly and you're delaying by a few hours or a day, over time that can create the impression that you're less interested.
That said, you don't need to reply instantly or artificially match his pace. But if you're reading his message and deliberately putting off your response to seem busier or less available - that can backfire. Better to reply when you can, but honestly, without games. If you're genuinely busy, say so, explain the situation. People respond better to honesty than to silence.
The key is to understand your own intention. If the delay is happening because you're actually caught up in things or just not in a texting headspace at that moment - great, that's normal. But if it's a conscious strategy, drop it. In the early stages of getting to know someone, the rhythm of communication shapes that first impression, and that's where the principle of reciprocity comes in.