A person's Moon moves about 12 degrees a day. Usually when we don't know someone's time of birth, we use 12:00PM, and so if the Moon is at 28 degrees Cancer at that time, it could be from 22 degrees Cancer up to 4 degrees Leo.
You also won't know the Ascendant, and very importantly imo, the house placements. You can put the other person's planets in YOUR houses, but you can't put your planets in the other person's houses because houses are determined by the Ascendant.
And that's it, really. Planets like Pluto, Saturn, Jupiter, Neptune and Uranus are very slow moving so won't change at all (or barely) during the day. Venus and Mercury can move 1-2 degrees in 24 hours, the Sun moves 1 degree (obviously
), Mars also about 1. None of these matter or change anything - unless you have an already distant aspect with one's Venus/Mercury, then it matters what time they were born on. If you notice one of these faster planets (Venus, Mercury, Mars) are at the last degree of a sign, enter the person's horoscope with 23:59 as the time of birth, so you can see if there is a sign change that day.
To sum it up: you can do a synastry, but completely ignore the other person's Ascendant (and Midheaven, all the house cusps, and Vertex as well), and only place the other person's planets in your houses - you can't do it the other way around.
You can even do a composite, but again, completely ignore all house placements, the Ascendant that shows up, and know the Moon placement will be kinda accurate but off by a few degrees.