How can water below a pH of 7 still be alkaline?
Classically, alkalinity is determined by $\ce{HCl}$ titration with methyl orange as indicator ( $\mathrm{pH}$ transition range $3.1 - 4.4$ ). IF some $\ce{HCl}$ is spent by lowering $\mathrm{pH}$ from $5.5-6.6$ to $\mathrm{pH}$ of noticing red colour, there is some nonzero alkalinity.
Note that at $\mathrm{pH} \approx 6.3$, the ratio $\dfrac{[\ce{CO2}]}{[\ce{HCO3-}]}$ is 1 : 1. (*)
Generaly, there is no direct relation between $\ce{pH}$ and maximal alkalinity, similarly as there is no direct relation between $\ce{pH}$ and $\mathrm{pH}$ buffer capacity.
But for typical water composition, containing $\ce{CO2/HCO3-}$ $\mathrm{pH}$ buffer, the alkalinity can be estimated from $\ce{pH}$ and expected $\ce{CO2(aq)}$ concentration, which is supposed to be in equilibrium with gaseous $\ce{CO2}$.
$$[\ce{HCO3-(aq)}] = K_{a1,\ce{CO2}}^{*} \cdot \frac {[\ce{CO2(aq)}]}{[\ce{H+(aq)}]}$$

(*) The  Wikipedia page for $\ce{H2CO3}$ has been recently misedited,  confusing $K_\mathrm{a2}$ and $K_\mathrm{a1}^*$(assuming 100% conversion of $\ce{CO2(aq)}$ to $\ce{H2CO3}$.