The short answer
If just your downstairs washer fills slowly, the trouble is right at that machine. Your house pressure is fine, or the upstairs washer and every faucet would be crawling too.
That's actually good news. It means you're looking at a short list of cheap, local causes instead of a whole-house plumbing problem.
in most cases it comes down to the mesh inlet screens where the hoses meet the washer, or a supply valve that isn't all the way open.
Both are DIY fixes. You need 15 minutes, a pair of needle-nose pliers, and a towel.
What's actually causing it
Let's walk through the usual suspects in the order a field tech checks them.
First, the inlet screens. Every washer has two tiny mesh filters sitting inside the ports where the hot and cold hoses screw on. Their whole job is catching rust flakes, sand, and scale so the valve doesn't jam.
Over 5 to 10 years they slowly pack solid. Flow drops from a strong rush to a sad trickle, and fill times balloon.
Second, the shutoff valves behind the machine. These get bumped constantly when a washer is moved or serviced. A valve turned 70 percent closed still runs water, just slowly, and nobody notices until the fills crawl.
Third, kinked hoses. Downstairs machines often live in tight closets or against basement walls. Push the washer back too far and a hose pinches behind it, choking flow with no leak to warn you.
Fourth, a failing inlet valve inside the machine. The electric solenoid that opens to admit water wears out. When it does, it may only open partway, and usually only on one temperature.
Fifth, and least likely, a genuine pressure problem on that branch line. This shows up mostly in older split-levels and basement laundry setups with undersized or corroded pipe.