Pushy, 4 bytes

Non-competing as the language postdates the challenge.

:Lh_

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This works by building the stack up to the final line, step-by-step, and printing the stages:

:    \ Input times do (this consumes input):
Lh   \  Push stack length + 1
_    \  Print stack items, space separated.

Pushy, 4 bytes

:Lh_

Try it online!

This works by building the stack up to the final line, step-by-step, and printing the stages:

:    \ Input times do (this consumes input):
Lh   \  Push stack length + 1
_    \  Print stack items, space separated.

Pushy, 5 bytes

Non-competing as the language postdates the challenge.

:&1+_

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This works by building the stack up to the final line, step-by-step, and printing the stages:

:       \ Input times do (consumes input):
 &      \   Copy the top item (does nothing first time, stack is empty)
  1+    \   Add one to it, or if the stack is empty, push 1 to begin the sequence
    _   \   Print the stack items, space-separated.

Ordinarily we would use h instead of 1+, but here we need 1+ so 1 is pushed when the stack is empty.

Pushy, 4 bytes

Non-competing as the language postdates the challenge.

:Lh_

Try it online!

This works by building the stack up to the final line, step-by-step, and printing the stages:

:    \ Input times do (this consumes input):
Lh   \  Push stack length + 1
_    \  Print stack items, space separated.

Pushy, 5 bytes

Non-competing as the language postdates the challenge.

:&1+_

Try it online!

Pushy, 5 bytes

Non-competing as the language postdates the challenge.

:&1+_

Try it online!

This works by building the stack up to the final line, step-by-step, and printing the stages:

:       \ Input times do (consumes input):
 &      \   Copy the top item (does nothing first time, stack is empty)
  1+    \   Add one to it, or if the stack is empty, push 1 to begin the sequence
    _   \   Print the stack items, space-separated.

Ordinarily we would use h instead of 1+, but here we need 1+ so 1 is pushed when the stack is empty.