  We present triple-axis neutron scattering studies of low-energy magnetic
fluctuations in strongly underdoped La$_{2-x}$Sr$_{x}$CuO$_{4}$ with $x=0.05$,
$0.06$ and $0.07$, providing quantitative evidence for a direct competition
between these fluctuations and superconductivity. At dopings $x=0.06$ and
$x=0.07$, three-dimensional superconductivity is found, while only a very weak
signature of two-dimensional superconductivity residing in the CuO$_2$ planes
is detectable for $x=0.05$. We find a surprising suppression of the low-energy
fluctuations by an external magnetic field at all three dopings. This implies
that the response of two-dimensional superconductivity to a magnetic field is
similar to that of a bulk superconductor. Our results provide direct evidence
of a very gradual onset of superconductivity in cuprates.
