The Ibrox side are favourites to win the Third Division - despite dropping points to Peterhead in last weekend's opener - after losing their status in the Scottish Premier League when the club was consigned to liquidation.
Ally McCoist's men are set to face Falkirk in the second round of both the Ramsdens Cup and the Scottish League Cup this month and will also compete in the Scottish Cup.
Despite the club being voted into the bottom tier of Scottish football, new recruit Sandaza is convinced the quality is still strong enough within the Rangers ranks to compete in all tournaments.
He said: "It must be our objective to win all the cups and go up to the Second Division.
"We have to live in the present and we are in this division just now but we must try to go up.
"That's why we are signing good players. We will go for it - that's for sure.
"Even in the Third Division, everything is very professional, including the quality of the training.
"We have signed good players from the SPL and other top leagues. Rangers want to have a good squad to try to achieve the cups this year.
"We are in the Third Division and we will respect the other teams that we play against.
"We had a draw in the first game and it was a lesson for us to show our best in every game."
Sandaza is one of a number of SPL-standard players signed by Rangers in recent weeks.
Former Hearts duo Ian Black and Kevin Kyle, as well as last season's Scottish PFA player of the year nominee Dean Shiels, have also committed themselves to the Glasgow giants.
Spaniard Sandaza was targeted by McCoist in January and says he declined to sign a pre-contract agreement at that time because of the financial uncertainty surrounding the club.
Rangers were forced to call in the administrators the following month, before Charles Green's consortium purchased the business and assets of the club in the summer after failure to exit administration via a Company Voluntary Arrangement.
Sandaza said: "I wanted to come in January and it didn't happen.
"In January, many people knew that they were going to have problems with the money and nothing was clear.
"That's why they couldn't pay the fee to St Johnstone. They offered me the pre-contract but nothing was clear.
"Now, even in the Third Division, it is a massive club. I'm sure we'll get back to the top division and we will be like Rangers was in the past.
"Ally McCoist called me two weeks ago and convinced me about the project of the club.
"That's why I have signed for four years. I'm happy to be here at this big club and with all these fans. It's brilliant."
Sandaza - who netted 18 goals for Saints last season - added: "I know I will score goals.
"I cannot say a target but I'm sure I will do my best and try to score as many as I can. I promise sacrifice and hard work.
"To play for Rangers, you will have more chances, more pressure. But I like the pressure and I'm sure I will score goals."
Sandaza was at Ibrox to meet fans at today's public sale of season tickets, with more than 25,000 season tickets already renewed.
The striker said: "It's a massive response from the supporters and shows how big this club is. Even in the Third Division, the supporters respond well."