Why did Danish people not "connect" with neighbor nations until Viking Age?

Before 450, Denmark was inhabited by the Saxons, Angles, and Jutes (from south to north). Geographically, the Jutes especially were the predecessors of the Danes. In the migration period, these three tribes left for Britain. Rome had abandoned Britain due to deteriorating conditions, which created a power vacuum. The Angles settled in Northeast Britain, the Jutes in southeast, and the Saxons in central and south Britain. The Jutes by far fared the best. Their territory became Kent, absorbed other Saxon kingdoms, married with the Merovingians. They became the first Bretwaldas. It's also notable that the Saxons may have been invited to Britain as mercenaries. After this migration period, we hear about the Danes in "Juteland". They were a distinct group of Norse who were related to the Swedes. They were especially freedom loving, hostile, and made up a large part of the Vikings. They were also some of the last of the Nors*m*n to convert to Christianity.

Before the Saxons migrated to England, they tried to settle in Gaul*. They were repelled by the Franks, who were allies of Rome. They managed to stay in Angers until being defeated by Chilperic in 469 (Haywood 86-7). The settlement of the Visigoths by Romans may have been in part against Saxons (Haywood, 88). In the 600s, Germanic Frisians took Dorestad on the lower Rhine. This probably contributed to the decline of the Merovingians (Haywood, 126). When the Frisii were kicked out of Dorestad, they took up pirating. Germanic pirates acted like their Viking sucessors. This included occupying an island at the mouth of a major river, which was an ideal base for piracy. The new Germanic migrants had become a part of the sea. The sea was safer than mainland Europe.

Just because Scandinavia was outside the reach of Roman Christianity (until Charlemagne), doesn't mean it was a wilderness. The Baltic Sea represented its own political sphere, like the Mediterranean. If it was really a wilderness, powerful war like tribes would not have emanated from it at regular intervals. The amber road had been active for Millennia, as well as numerous trade routes across Europe. Still, people tend not to migrate unless they are under pressure. Swedes did not directly follow the path of their German predecessors because from around 200 A.D., Germans had been developing sea power. They did try to make inroads into Europe, but were blocked by Franks and Goths. Still, the Frisii and Saxons had continental territories until Charlemagne.

The first Swedish kingdom also formed around 750. This was also around the time that the Rus became a major force on the Dneiper river. These first Swedish kings were also the first kings of Norway c. 900. From about 750-1000, Scandinavia was full of tribal warfare and fledgling kingdoms. It just so happens that that 750 is about the time that Vikings appear in Western Europe. I haven't seen it mentioned, but it appears that the settlers were an effect of the state building of Scandinavia, 750-900.

The inherent independence of the Baltic trade is later evidenced by the Hanseatic League.

*I'm pretty sure this is in Haywood. I don't have it in front of me, and its not in my notes.

A few answers have pointed out the relative ease that you can get to England, so I won't go that route with this answer. I'll go with wealth and militancy, along with some revenge.

England could be recognized as an easier conquest during this time frame, repeated war and intervention from a variety of sources left England relatively weak to foreign invasion. Æthelred and several 'pre-england' kings paid massive ransoms to the Danish (referred to as 'Danegold'), the isle was truly ripe for the pickings and they had the wealth to pick. Reversely, much of the Germanic tribes to the south were much more nomadic and lacked the wealth to pay such ransoms.

There is also some politics involved here. Francia was the frankish nation within Europe and at it's hieght under Charlemagne had occupied everything in now current day France, to Italy, and Germany. They had defeated superior foes such as the Umayyad Caliphate and would put up tough resistance to invaders. Ragnar Lodbrok invaded Francia and had general success, but eventually made his way up to England after some tribute and military stalemates (Siege of Paris (885–86)). King Ælla of Northumbria captured and killed Ragnar (pit of snakes is the legend). In the name of revenge, The Great Heathen Army (mostly Danish Vikings) attacked England and would eventually settle there.

Oddly, this revenge over the killing of Ragnar by an pre-English king was likely a good reason they hit England as hard as they did.

Poland - This wasn't an easy target like you suggest...home to the Goths, a semi-nomadic people that were extremely warrior like, would put up a big fight and present little wealth to the victors.

Scythia - There is much lost history here, but if you go into lithuania and further south, you find the Scythian peoples. http://our-russia.com/1466750716/expedition-kyzyl-%E2%80%93-kuragino-lost-tribes-and-origins These were also a nomadic people with not as much wealth to plunder, but also a heavily warlike people that gave rise to the legendary Amazon warriors. Considered by many (Roman/Greek sources) to be warriors without equals (from the link ""No invader who comes against the Scythians can ever escape and none can catch them if they do not wish to be caught.“ – Herodotus").

To get to any real wealth, one would have to venture as far south as Byzantine and Constantinople (which the Swedish vikings did, becoming the Varangian guard).

To your question:

Why did they choose this much riskier path when they could have chosen much safer paths?

A bit of a mix of the other paths having little wealth but great resistance, and a little bit of revenge.