You can probably cast Simulacrum using a familiar
Obviously, the familiar itself cannot cast a seventh level spell as it lacks the Spellcasting feature. You as a wizard can cast touch spells through your familiar just fine. However, Simulacrum is a bit special. It states
You shape an illusory duplicate of one beast or humanoid that is within range for the entire casting time of the spell.
And the material components are
snow or ice in quantities sufficient to make a life-size copy of the duplicated creature; some hair, fingernail clippings, or other piece of that creature's body placed inside the snow or ice; and powdered ruby worth 1,500 gp, sprinkled over the duplicate and consumed by the spell
All of which implies that you do not just need to touch the target, you have to stick around for 12 hours because you are building a snow-creature from the material components, which then is transformed into the target's likeness.
It is possible that a familiar such as an imp or quasit could form such a creature. Unfortunately you cannot deliver touch spells through such a familiar as a wizard. It is unlikely that any of the "standard" familiars afforded by the spell, such as a spider, would be able to form such a snow-effigy.
However, if you were building the effigy outside (i.e. someplace else within the 100 foot range), and would during that time be in "touch" range with your vicitm via your familiar, and also have their hair, nail clippings etc. around, I think it could work.
On possible stumbling stone is that the implication is you need to have the target around to see how they look like, when you are shaping the duplicate. This, you could not do through your familiar, because the spell says:
Additionally, as an action, you can see through your familiar's eyes
And the PHB under Longer Casting Times (p. 202) says
When you cast a spell with a casting time longer than a single
action or reaction, you must spend your action each turn casting the spell
So you could not cast the spell and at the same time look through the eyes of your familiar as both cost your action. However, the requirement of seeing the target is not explicitly stated by the spell, and therefore not demanded by rules as written.
Talk with your DM. Maybe he or she is of the lenient kind and will rule it is sufficient you took a good look at your victim before your started, to allow this stratagem. I likely would.