Converting a galvanometer into an Ammeter
how can we successfully measure current when the deflection of the
  needle is going to always be maximum due to the passage of Ig current
  (which is the current that causes maximum deflection)


You understood this part wrong. Maximum deflection occurs at Ig(max). If Ig is less than Ig(max), the needle will stay somewhere in between.

Deflection of needle is not always going to be maximum.

When you are designing the ammeter, you need to select a value of Rs depending upon the max current you intend to measure. For ex - an ammeter which can measure current up to 1 A will use a larger value of Rs as compared to an ammeter which can measure a current up to 100 A.

For the ammeter rated for 1 A, the Ig(max) value will be reached only when you are allowing 1 A through the ammeter. For the ammeter rated 100 A, Ig(max) will be reached when measured current is 100 A.

For current values lesser than rated values, the current through galvalometer will be less than Ig(max) and hence you will be able to measure the current through the ammeter. If you pass a current higher than rated value (eg - 2 A through 1 A rated ammeter), the needle will show full deflection and there is no way of knowing the exact value of current passing through it.