Place the sign using /setblock ~ ~ ~ minecraft:standing_sign 0 replace {Text1:"{\"score\":{\"name\":\"@s\",\"objective\":\"scoreboard\"},\"color\":\"black\",\"extra\":[{\"text\":\"←invisible\",\"color\":\"black\"}]}",Text2:"{\"text\":\"random text\",\"color\":\"black\"}",Text3:"{\"text\":\"random text\",\"color\":\"black\"}",Text4:"{\"text\":\"random text\",\"color\":\"black\"}"} or
[Demo] This only affects the "score" text type.
To Reproduce
/scoreboard objectives add scoreboard dummy
/scoreboard players set @p scoreboard 1
/setblock ~ ~ ~ minecraft:standing_sign 0 replace {Text1:"{\"score\":{\"name\":\"@s\",\"objective\":\"scoreboard\"},\"color\":\"black\",\"extra\":[{\"text\":\"←invisible\",\"color\":\"black\"}]}",Text2:"{\"text\":\"random text\",\"color\":\"black\"}",Text3:"{\"text\":\"random text\",\"color\":\"black\"}",Text4:"{\"text\":\"random text\",\"color\":\"black\"}"}
or/give @p minecraft:sign 1 0 {BlockEntityTag:{Text1:"{\"score\":{\"name\":\"@p\",\"objective\":\"scoreboard\"},\"color\":\"black\",\"extra\":[{\"text\":\"←invisible\",\"color\":\"black\"}]}",Text2:"{\"text\":\"random text\",\"color\":\"black\"}",Text3:"{\"text\":\"random text\",\"color\":\"black\"}",Text4:"{\"text\":\"random text\",\"color\":\"black\"}"}}