How can I get rid of a delay when an animation plays?

I'm trying to make an animation script for being idle and walking. I know that I can change the default animation, but I'm looking to do something else with this. My problem is that there's a delay between the player moving and the animation playing. I'm also using a script inside ServerScriptService instead of a local script because I don't think a local script would animate on both client and server(if it does please let me know). If it's because of an issue with the animation itself, please let me know and I'll fix that.

game.Players.PlayerAdded:Connect(function(plr)
    repeat wait() until plr.Character
    local char = plr.Character
    local Humanoid = char.Humanoid


    local idle = Instance.new("Animation")
    idle.AnimationId = "rbxassetid://7052225614"
    local idletrack = Humanoid:LoadAnimation(idle)
    local move = Instance.new("Animation")
    move.AnimationId = "rbxassetid://7052226982"
    local movetrack = Humanoid:LoadAnimation(move)

    local function playAnimation(animName) 
        if animName == "move" then
            movetrack:Play()
        end
        if animName == "idle" then
            idletrack:Play()
        end
    end

    local function stopAnimation(animName) 
        if animName == "move" then
            movetrack:Stop()
        end
        if animName == "idle" then
            idletrack:Stop()
        end
    end

    playAnimation("idle") --To load it when the player spawns

    Humanoid.Running:Connect(function(speed)
        if speed > 0 then
            if not movetrack.IsPlaying then
                stopAnimation("idle")
                playAnimation("move")
            end
        else
            if speed == 0 then
                if not idletrack.IsPlaying then
                    stopAnimation("move")
                    playAnimation("idle")
                end
            end
        end
    end)
end)