Step 1: Trace the villous timeline because fetal blood flow needs vessels inside the villi plus a beating heart.
Step 2: Tertiary villi, the first to contain fetal blood vessels, appear about day $21$, coinciding with the onset of the fetal heartbeat. This pairing of vessels and pump is what launches fetoplacental circulation, around days $20$ to $22$.
Step 3: Earlier dates fail: day $7$ is just blastocyst attachment, days $11$ to $13$ cover lacunae and primary villi without fetal vessels, and days $25$ to $26$ overshoot the milestone.
\[\boxed{\text{20 to 22 days}}\]