Start with sands of time, lost artifact, and 3x mana 2x health pots.

Sands of time gives you early game power and mana regen. It also gives you 10% cooldown reduction which is an important stat on merlin.

(Alternatively you can go sands of time and T1 boots along with 3x health and mana pots if you want the extra movement speed.)

Lost artifact start allows you to have more mp5 along with early game power but you will need to be more cautious with positioning as you wont have the movement from boots early game.

Merlin in the early levels doesn't have much movement and even once he hits lvl 3 to put a point into his flicker (3rd ability) it has a base 22 second cooldown. Because of this most players will focus and dive merlin due to the lack of mobility. Beads are invaluable on Merlin as even if you get caught out of position you just slam on your beads to avoid hard CC.

Your 2nd relic once you hit lvl 12 should be Aegis for primarily the same reason above. It serves as a buffer if you are caught out. Timing your Aegis takes getting used to so if you want something else Heavenly wings is good as it makes you immune to slows for 5 seconds which are strong at locking down Merlin.

Blink is also good for immediately repositioning yourself.

I would recommend finishing lifesteal boots before fully building Charon's Coin. However you do want to get Coin early as you will need 10 god kills/assists to finish stacking it.

Your 2nd item should be Spear of the Magus. It was recently buffed and now gives lifesteal so combined with your boots you will have 20% magical lifesteal. Its passive also works very well on Merlin as he throws out abilities very regularly.

3rd item Should be Chronos Pendant which gives 20% cooldown reduction. Mainly just for the cooldown to help you constantly throw abilities while also giving you more mana. This will also bring your Flicker base cooldown down to 14 seconds by the end of the game Flicker will have a 12 second cooldown allowing you to be very mobile.

4th item can be Soul Gem if you want the added healing while also giving you max cooldown (40%) a little early. However if you do build life gem once you finish your starter item you will be overcapped on cooldown reduction since upgraded starter gives 20% instead of 10%.

If you want extra power Rod of Tahuti is another good choice for your 4th item slot. It gives 2x as much power as Soul Gem while also making you do extra damage on anyone below half health.

If the enemy team is heavily reliant on healing Divine Ruin is very useful on Merlin since its very easy to proc.

After selling your boots and buying the speed potion you will have a open slot. If your 4th item was Soul Gem then your final item should be Rod of Tahuti. If your 4th item was Rod then your final item should be between Soul Gem or Spear of Desolation. Spear gives you extra penetration while also letting you spam your abilities via the Spear's passive.

Once you hit level 20 you will be able to finally upgrade your starter item. Pendulum of Ages will give you a little extra power depending on how much mana you are missing.

While a little more of a gimmick item with the recent buffs Alternate Timeline isn't an awful choice. It will give you quite a bit less power it does give you some protections. Getting this will also make it so you aren't wasting that 10% cooldown from earlier as by this point of the build you likely already reached 40%.

Overall Pendulum of Ages is a better pick but if you do pick up Alternate Timeline it can very likely save you at some point.