#!/usr/bin/env jq -n -R -f

# Get seeds
input | [ match("\\d+"; "g").string | tonumber ] as $seeds |

# Collect maps
reduce inputs as $line ({};
  if $line == "" then
    .
  elif $line | test(":") then
    .k = ( $line / " " | .[0] )
  else
    .[.k] += [[ $line | match("\\d+"; "g").string | tonumber ]]
  end
)

# For each map, apply transformation to all seeds.
# seed -＞ ... -＞ location
| reduce ( to_entries[] | select(.key != "k") .value) as $map ({s:$seeds};
  .s[] |= (
    # Only attempt transform if element is in one of the ranges
    [ . as $e | $map[] | select(. as  [$d,$s,$l] | $e ＞= $s and $e ＜ $s + $l) ] as $range |
    if ($range | length ) ＞ 0 then
      $range[0] as [$d,$s] |
      . - $s + $d
    else
      .
    end
  )
)

# Get lowest location
| .s | min

Some comments:

• A nice use of input first to get the seeds, then inputs to get remaining lines.

#!/usr/bin/env jq -n -R -f

# Utility function
def group_of($n):
  ( length / $n ) as $l |
  . as $arr |
  range($l) | $arr[.*$n:.*$n+$n]
;

# Get all seed ranges
input | [ match("\\d+"; "g").string | tonumber ] | [group_of(2)] as $seeds |

# Collect maps
reduce inputs as $line ({};
  if $line == "" then
    .
  elif $line | test(":") then
    .k = ( $line / " " | .[0] )
  else
    .[.k] += [[ $line | match("\\d+"; "g").string | tonumber ]]
  end
)

# For each map, apply transformation to all seeds ranges.
# Producing new seed ranges if applicable
# seed -＞ ... -＞ location
| reduce (to_entries[] | select(.key != "k") .value) as $map ({s:$seeds};
  .s |= [
    # Only attempt transform if seed range and map range instersect
    .[] | [.[0], add, .[1] ] as [$ea, $eb, $el] | [
      $map[] | select(.[1:] | [.[0], add ] as [$sa,$sb] |
        ( $ea ＞= $sa and $ea ＜ $sb ) or
        ( $eb ＞= $sa and $eb ＜ $sb ) or
        ( $sa ＞= $ea and $sa ＜ $eb )
      )
    ] as $range |
    if $range | length ＞ 0 then
      $range[0] as [$d,$s,$l] |
      # ( only end ) inside map range
      if $ea ＜ $s and $eb ＜ $s + $l then
        [$ea, $s - $ea], [$d, $eb - $s ]
      # ( both start, end ) outside map range
      elif $ea ＜ $s then
        [$ea, $s - $ea], [$d, $l], [ $s + $l, $eb ]
      # ( only start ) inside map range
      elif $eb ＞ $s + $l then
        [$ea + $d - $s, $l - $ea + $s ], [$s + $l, $eb - $s - $l]
      # ( both start, end ) inside map range
      else
        [$ea + $d - $s , $el]
      end
    else
      .
    end
  ]
)

# Get lowest location
| [.s[][0]] | min

Some comments:

• Since iterating across all seeds naively would take forever, iterating over seed ranges instead.
• It's nice that JQ can neatly produce extra elements: [1,2,3] | [ .[] | if . == 2 then . * 10 + 1 , . * 10 + 2 else . end ] -> [1, 21, 22, 3]
• There is probably a more compact way of expressing all the conditions and produced outputs.