Due to the Pohlig-Hellman algorithm, the hardness of discrete logarithms is dominated by the largest prime factor $\ell$ of the group order $n$. In particular, one typically works in a subgroup of order $\ell$ of the curve group, since the additional factors $h$ in a generator's order would not significantly contribute to security.
In that, note that $\ell$ depends on the group order $n$: You cannot just decide for some order $\ell$ and then find a point $G$ of that order on an arbitrary fixed curve, since it general such a point will not exist. (However, there is the complex multiplication method, which generates a new curve of given order.)
Therefore, steps 2 and 3 of the algorithm given in the question must be swapped: You first compute the curve group order $n$, factor it, and determine $\ell$ from the factorization. (And if $\ell$ is too small, you should start over with a new curve. For example, Curve25519 has cofactor $h=8$.)
Other than that, the algorithm is fine, except that you might want to check whether $G=\infty$ and start over in that case. However, this only happens with probability $1/\ell$, so it should never occur in practice for cryptographically-sized curves. (Moreover, you would compute and factor the group order only once and find a good $P$ afterwards, but this does not impact the expected runtime much as $P$ usually is good at the first try.)
Thus, we have the following algorithm:
- Compute the curve order $n=\#E(\mathbb F_p)$.
- Factor $n$ to determine its largest prime factor $\ell$. (Note that you do not need to fully factor $n$: If the remainder after removing a few "small" divisors is not prime, the cofactor is going to be too big anyway.)
- Compute the cofactor $h=n/\ell$. If $h$ is "too big", start over with a new curve.
- Choose a random point $P\in E(\mathbb F_p)$ and let $G=[h]P$.
- If $G$ is the point at infinity, go back to choosing a new $P$. Else, $G$ has order $\ell$.
