Melee builds on insanity difficulty?

Maybe, but it's definitely not at the start of the game. As you've found, the enemies will tear you to shreds if you try to chase after them out of cover.

It may be possible later in, but it's too early to tell from the trial how the mid to late game will play out.

I tried going Vanguard since it's always been my favorite ME class, but using Charge at the wrong time is basically suicide in Andromeda. I do agree with ayenari though, it's probably something that becomes more viable later in the game.

I might remember wrong, but Charge wasn't viable at level 1 in ME3 either. In ME:A, I found that Vanguard starts to work around level 4, I guess it will be solid around level 8-9. I went with an AR (Mattock) instead of a shotgun to complement the melee weapon. 100% melee won't be viable, there are flying enemies.

It was certainly a pain in bare bones form in ME3, it just wasn't a problem if you were importing an ME2 save and could spruce it up immediately. I'm going to have to remember how to shoot vaguely straight aren't I?

I think melee should be viable here are some things to keep in mind:

First of all you obviously need to use charge to get in range of the enemy fast without error and you are invincible while charging at enemies, so you would always go in with charge OR you use cloak. In Andromeda you can Charge at flying enemies and you can hit them wth your melee because you can use melee while you are airborne.

Vanguard profile has a passive called Siphoning Strike which makes your melee attacks restore shields, here are full details of a level 1 Vanguard profile:
+20% Melee Damage( you want this )
+50% Melee Force ( this will stagger enemies so they won't retaliate )
+10% Biotic Recharge Speed ( faster charge )
+20% Power Shield Cost Reduction ( if you decide to spec nova into shield cost but I would not recommend you to use Nova at all, as that is not a part of a melee build )
+10% Max Shields
Siphoning Strike: Melee attacks restore shields. ( this is your survive tool for melee )

So melee should become viable as soon as you get your vanguard profile which you don't get yet during the first mission.
I would also recommend using backlash biotic shield to buy yourself some time to get in cover or to wait for your charge to recharge. 
Also I think Cloak would be a nice third power as another tool to get to safety or reengage on the enemy and cloak also provides melee damage. 

Play pattern would go Charge at enemy OR Cloak and engage on enemy => kill them with melee => use backlash to deflect all incoming damage => Repeat.

You don't want to spec into ANY power damage because you want to kill things in melee, your cloak and backlash doesn't scale with power damage at all and charge will just have token damage, but cloak and charge both spec into giving more melee damage and backlash is completely defensive skill. You want to take passive for more melee damage like fitness martial artist.

Im also playing vnaguard and i found its best to use it to kill fringe enemys and pick people off. I found flamethrower is a really good power to take down enemys it wrecks armour and it makes a good impact on shields as well

Thankss for the replies guys. Lots of good info here .