Most licensing delays are not caused by slow authorities. They are caused by starting approvals in the wrong order, because several permissions require another one as an input.
The chain that causes the damage
In many cities, the fire NOC is required before the municipal trade licence will issue. Pollution consent, where applicable, is sometimes required before the fire NOC. Each of those can take several weeks on its own. Run them one after another, starting late, and a path that could have taken two months takes six — while you are paying rent on a site you cannot trade from.
The rule: start the slow, dependent ones the week you sign
Fire NOC and pollution consent should be applied for as soon as the lease is signed and the layout is fixed. They do not depend on your fit-out being complete, and they are the two most likely to sit in a queue. FSSAI, GST and Shop and Establishment are comparatively fast and can run in parallel later.
What runs in parallel and what cannot
Parallel: FSSAI, GST, Shop and Establishment, signage, weights and measures, music. Sequential: anything that needs premises approval or a fire clearance as an input — typically the trade licence, and in many cities the eating-house permission.
Liquor, if you are applying, sits outside this logic entirely. It is the longest path in almost every state and should be started before anything else if the business depends on it.
Build a dated path, not a list
Work backwards from your intended opening date. Put each permission on a timeline with its expected duration and its prerequisite. Anything with a dependency gets its start date set by its prerequisite's finish date, not by convenience. The permissions with no dependencies fill the gaps.
Timelines vary widely by city and by season, so use your own enquiries rather than published estimates. The discipline that matters is the ordering, which does not change.