What height would humans reach if we kept growing through our whole development period (i.e. till late teens/early twenties) at the same pace as we do during our first month?

Maria

Tall.

According to the National Center for Health Statistics, the average newborn's height (length) is approximately 0.5 meters,[1]or 0.56 meters in heels. or a quarter of the diameter of the Death Star thermal exhaust port.

From this initial height of 0.5 meters, they grow to about 1.5 or 2.0 meters:

Babies grow fastest right after they're born. During their first month, infants grow about 4.4 centimeters, ten times their growth rate during their early teenage years.

In Maria's scenario, this growth rate continues until about age 20:

Let's follow that child's growth over the years.

By its first birthday, the baby would be a meter long:

At 2 years and 3 months, the kid would reach 169 centimeters (5'7"), the average adult height in the US.

By age 3, we'd have a 2.08 meter (6'10") toddler, taller than Darth Vader ...

... and much taller than Yoda:

By age 4, the child would be nearly nine feet tall, able to dunk a basketball without jumping.[2]A 7'8" Harlem Globetrotters player can almost dunk without jumping, so the threshold for a clear no-jump dunk is probably around 8 feet.

A few months later, the kid would surpass Robert Wadlow to become the tallest human in history.

At age 5, the child would be $ \pi $ meters tall (10'4"):

At age 7, the child would be 4.2 meters tall, able to stare down a T-rex:

By age 10, the child would be 5.8 meters tall (19 feet). If we assume these giants are proportioned like adult humans, this kid would weigh over a metric ton.

Actual humans wouldn't be able to grow to such heights. Thanks to the square-cube law, our bones would be too thin to support our weight and our hearts would be unable to pump blood around our bodies. Even breathing would be difficult; we might be able to position ourselves to keep our airways opened, but to breathe in a lungful of air would require very high airflow rates; we'd experience tornado winds all the way down our airways.

Our giant would reach a final height of between 10 and 12 meters, assuming growth tapered off around age 20. At that height, they'd be able to comfortably dunk a basketball while keeping one hand on the court outside the three-point line.[3]A creative NBA 2K3 mod shows us what that player might look like.

In addition to the insurmountable health problems, someone with this rapid growth rate would face another hardship.

To ride roller coasters, you have to be above a certain minimum height. However, they generally also have a maximum height.

Bizarro, a coaster at Six Flags New England, has a minimum height of 137 cm (4'6") and a maximum height of 193 cm (6'4"). Our child would be tall enough to ride Bizarro at age 2 ... and too tall by age 3. Their coaster-riding window would last only 387 days.

It's a sad truth: Roller coasters just aren't for everyone.