Charcoal, 14 bytes

× ³⁰Ｆ³⁰«↙+Ｍ‽³→

Try it online! Link is to verbose version of code. Explanation:

× ³⁰            Print 30 spaces (forces the desired indentation)
    Ｆ³⁰«        Repeat 30 times
        ↙+      Print a `+` and move down and left one square
          Ｍ‽³→  Move right a random number of squares from 0 to 2

Would be only 10 bytes if there was no initial indentation requirement.

Charcoal, 14 11 bytes

× ³⁰Ｆⅈ✳～‽³+

Try it online! Link is to verbose version of code. Explanation:

× ³⁰        Print 30 spaces (forces the desired indentation)
    Ｆⅈ      Repeat the same number of times
      ✳～‽³  Move a random downward direction after printing
          + Print a `+`

Would be only 10 8 bytes if there was no initial indentation requirement.

Charcoal, 10 bytes

Ｆ³⁰«↙+Ｍ‽³→

Try it online! Link is to verbose version of code. Explanation:

Ｆ³⁰«        Repeat 30 times
    ↙+      Print a `+` and move down and left one square
      Ｍ‽³→  Move right a random number of squares from 0 to 2

Charcoal, 14 bytes

× ³⁰Ｆ³⁰«↙+Ｍ‽³→

Try it online! Link is to verbose version of code. Explanation:

× ³⁰            Print 30 spaces (forces the desired indentation)
    Ｆ³⁰«        Repeat 30 times
        ↙+      Print a `+` and move down and left one square
          Ｍ‽³→  Move right a random number of squares from 0 to 2

Would be only 10 bytes if there was no initial indentation requirement.