Hebrews 9:18

So even the first covenant was inaugurated with blood. ¹ 

This is why even the first covenant was not put into effect without blood.

Therefore even the first covenant was not inaugurated without blood.

That is why blood was required under the first covenant as a proof of death.

Even the first plan required a death to set it in motion.

So that even the first agreement was not made without blood.

Hence not even the first covenant was inaugurated without blood.

Therefore not even the first covenant was dedicated without blood.

So even the first covenant was inaugurated with blood. ¹ 

¹ sn The Greek text reinforces this by negating the opposite (“not even the first covenant was inaugurated without blood”), but this double negation is not used in contemporary English.