I have been tent camping over 30 years. All but the last two in a tent like yours. I own two tents of that design and a white canvas wall tent.
One of my old tents like yours is over 30 years old. Non of them where what I would call water proof. The problem is with the external frame design.
The frame going through the loops on the eaves creates a pocket which catches rain. and will hold enough water to break a pole. The water will sit there and soak through..
If you want to keep using this tent you need a rain fly. As other have said.
Set the tent up ,measure from ridge to eave and add 2 ft. than double that measurement.
Next measure front to back and add 7 ft.
Find a poly tarp close to that size. I suspect you will be some where around 12 x20. I buy a white tarp for all my flys and only use them for that purpose.
Once you get your tarp lay it over the set up tent.
Position it two feet from eve each side and 1ft extra in back.
The other 6 ft is at the door and creates a porch like area.
Next take a marker and mark all four corners where they touch the frame.
Write front and back on the edges. This makes it easy to throw the fly over the tent , just match the marks and you know its in the right spot .
Now I like to set my tent up with a tree front and back aligned with center. Than I run a ridge line over the tent, throw the fly over that and tag out the edges all the way around. If no trees, throw six mental fence posts in your truck.
The water dripping two feet way from the walls is key.
I may let the fly touch the ridge but nothing else. I like a air pocket between tent and fly. This allows tent to dry after a storm if it clears up.
Also if the fly is not tied to the tent. If it is raining when you break camp you have a nice cover to work under while you take your tent down.
In all the years in the heavy down pours or wind storms I have never got wet.
Once you get the system you will be happy.