It is indeed possible to build bridges like this. They have a weightlimit though.
Example here :
|\ ________ /|
That's the bridge. The two " | "s are marked as A and B. A and B are hammered into the ground and can take weight (W) up to a point depending on how far the logs are hammered into the ground (D), how long they are (V) and how dense the ground is per CM (P). The farther down in the earth they are the more frictionstability (F) they offer.
Other components like the ropes (R) can also take a certain weight (W) until they rip.
To build a bridge that is supposed to carry a certain weight, let's say 3 people (H) that weight 80kg (M) each and the bridge has to be 20 meters (Q) long you need to calculate the following :
F = x
x = (V - D) * P cm
M = 240 kg
V = Z cm
D = Y cm
P = 3 kg per cm after 50 cm exp. +2 on 50 cm and every 10 cm after that
D = 50 cm * 3 kg = 150 kg
D = 5 x 10 = 50 + 150 = 200 kg < M
D = 7 x X = 40 | 40 / 7 = 5.71 ~ 6
D = 50 cm + 10 cm + 6 cm = 66 cm
D = 66 cm
Now we know that the log has to be hammered 66 cm into the ground to support the target weight of 240 kg (D). To calculate how tight the ropes have to be to not swing / bulge would take way too long so I'm going to keep it simple and simply estimate that the log should be about 2 meters above ground to support a somewhat stabile building. This sets the unknown variable of, let's call it "U" to 2 meters.
U = 200 cm
V = U + D | 200 cm + 66 cm = 266 cm
V = 266 cm
This means we need 4 logs that are 266 cm long to support a weight of 240 kg. Since the ropes and boards will weight, let's say 50 kg this bridge will effectivelly only support 190 kg, speaking 2 heavy adults and a kid.
I planned to do a full calculation but this took longer than expected. I hope this gave you guys about the idea what you need to calculate to build a suspension bridge like OP suggested.
TL;DR : You can build these bridges with real physics