Visitor: 

I have two hesitations about TULIP. It starts with total depravity while the Bible starts with God, and man made in his image. Second, we as finite beings, live in a time bound world. We cannot begin to explain a perspective from outside of time. God knows the end from the beginning but we make choices everyday. We are not puppets. We don’t explain away these choices because God knows the end. As Joshua said, Choose you this day who you will serve.

Response:

It does not start with Total Depravity.  TULIP is just an acrostic to help people remember the five points.  That's all.  Consider how does Heidelberg Catechism start? how does WCF start? Michael Horton once said, "Covenant, not predestination [and not total depravity!], is the warp and woof of Calvinism" (Beyond The Bounds).

Also all Calvinsts believe we have a will and make voluntary choices.  God created man with natural liberty (not coerced) but after the fall while man still has natural liberty, his will became corrupt.  When a Calvinist says man has no free will he does not mean God coerces him but rather that his fallen will is captive to sin and cannot do otherwise apart from regenerating grace.  

Next, when Joshua said "choose this day whom you will serve", I would encourage you to look at the immediate context.  The people declared they would choose God, but Joshua answers, "But Joshua said to the people, “You are not able to serve the Lord, for he is a holy God".  Joshua 24:19. 

So commanding people to do something does not mean they are able without the aid of grace.  If you borrowed lots of money, but squandered it and can't pay it back the bank still calls you to repay. It is your responsibility. Likewise our inability to obey Gods commands does not alleviate us of our responsibility. Do you always love God with all your heart?  

Paul says as much in Roman's 3:19-20

Now we know that whatever the law says it speaks to those who are under the law, so that every mouth may be stopped, and the whole world may be held accountable to God.  For by works of the law no human being[a] will be justified in his sight, since through the law comes knowledge of sin.

I.e. commands do not reveal our ability but our sin, our inability to obey.  We are unable because we are unwilling. We (in our fallen unregenerate state) "love darkness, hate the light and will not come into the light (John 3:19-20).  That is why Jesus said, "the Spirit quickens; the flesh is no help at all.... This is why I told you that no one can come to me unless it is granted him by the Father.” John 6:63, 65

The Spirit must work to open our blind eyes, unplug our deaf ears and soften our hardened stony heart... or we would never believe.  Salvation is of the Lord from first to last.  We cannot ascribe our repentingbor believing (even partly) to our own wisdom, humility. Sound judgment or good sense, but to Christ alone.  (See 1 Cor 1:29-31)

Shalom.