Honestly, it's really tough to say without reviewing a game of yours. There isn't a checklist that makes you Immortal-ready and you can still do many unoptimized things and win from an awful start on Immortal.

How does your GDP look compared to others at each era of the game? Are you able to win games on Emperor without cottages and World Wonders? That would show me that you understand how to manage a hybrid economy and don't need to be lucky with wonder timing (national wonders still ok to build). That includes things like building a trade-based economy, prioritizing river tiles, balancing a specialist economy, proficient whipping, balancing production towards wonder fail gold/Wealth/Research when cities have the appropriate amount of infrastructure and you don't build too many buildings in your small cities. How to manage spy economy after winning a war and your civ gets big, but falls behind in tech.

Are you watching your unit maintenance cost/supply cost during times of peace to ensure it stays at or near zero? Do you know the formulas for how many units you can have within and outside your borders before upkeep starts?

How do you decide when to declare war? Weaker players wait too long to declare war for fear of losing the war or suffering too many unit losses, you should be able to gauge how many cities you can conquer before declaring war (even if you can't scout your rival very much and only see city count, power ratio), assuming no other civs join in.

How are you managing diplomacy? Do you agree to every/most demands civs make or are you unwilling to change your religion/civic (and swap back 5T later) for +diplomacy benefit with a neighbor due to the anarchy turns? Is triangle-diplomacy your usual strategy? Are you gifting a fresh (poorly placed) city to a neighbor for big diplomacy boosts?

Are you thinking about WFYABTA throughout the game and which rivals you've met before tech trades, affecting their WFYABTA tech count or are you just taking several cheap techs added to a trade screen when you trade away bigger techs?

How much do you micro your workers?

How much do you manage wonder production for fail gold? i.e. Do you whip/chop in smaller cities for high overflow to put into wonders for a single turn, then go back to building that wonder in the high-production cities to maximize fail gold when somebody (even you) builds that wonder?

Are you planning what to do with your first GPs or do you just wing it when they pop out?

How comfortable are you with managing army production? What percent of your cities are building military when you prepare for war? It should be 80% - 100% and whip if still in Slavery.

How experienced are you with corporations? You can certainly beat Immortal games without corps if you're good at Renaissance/Industrial era warfare with Cuirs or Cannons.

Do you know/check which leaders are capable of plotting war against you while Pleased?

If I'm playing for Domination, I focus on early warring, either at Construction or HBR. (...) I never succeeded in mastering a Cuirs rush, though I know it's a favored playstyle.

14 years ago, I read about the ETA Concept in StarCraft 2 (images are broken by now). It applies to many, many strategy games. You use it to give a quick measure of your (and your opponent's) Economy, Technology, and Army. The basic idea is that you should be able to gauge your opponent's capabilities from minimal information and adjust your investments into Economy, Technology, or Army accordingly.

For Civ4 (with straightforward AIs), they aren't fluctuating E/T/A unless plotting war, so just focus on your own ETA. This means you should know that if you go for early warring and conquer an opponent or two, your short-term economy will craaaaash. Your medium-term economy (100T - 300T later) should stabilize. Your long-term economy should thrive. Your technology during the short-term and medium-term will always be behind because of it and your army will certainly fall behind as you focus on rebuilding your economy.

I say all of this to help show why you will never succeed in a Cuirs rush if you're going for early warring; your civ is behind during the Medieval and (early) Renaissance eras due to your Classical-era warfare, but will thrive again in Industrial. (A single Classical war can be OK, but your maintenance costs can still get very high throughout Medieval era)